Washington (CNN) Republicans are preparing for the penalty phase of the 2016 election.

The next Republican civil war came into greater focus over the weekend when party chairman Reince Priebus threw a thinly veiled warning at former GOP 2016ers who haven't yet endorsed Donald Trump: "Get on board" or face penalties if you ever seek the presidency again.

The nudge -- aimed at Republicans such as John Kasich, Ted Cruz and Jeb Bush -- was no off-the-cuff expression of frustration. Several Republican party chairs in early voting states told CNN that Priebus has spent days talking about enforcing the pledge that all 17 GOP candidates signed at the outset of the 2016 primary to support the eventual nominee.

"I can't tell you how many people have asked me, 'What are you going to do about these candidates that are not keeping their promise?'" Iowa GOP chairman Jeff Kaufmann told CNN Monday.

Photos: Donald Trump's rise Photos: Donald Trump's rise President-elect Donald Trump has been in the spotlight for years. From developing real estate and producing and starring in TV shows, he became a celebrity long before winning the White House. Hide Caption 1 of 37 Photos: Donald Trump's rise Trump at age 4. He was born in 1946 to Fred and Mary Trump in New York City. His father was a real estate developer. Hide Caption 2 of 37 Photos: Donald Trump's rise Trump, left, in a family photo. He was the second-youngest of five children. Hide Caption 3 of 37 Photos: Donald Trump's rise Trump, center, stands at attention during his senior year at the New York Military Academy in 1964. Hide Caption 4 of 37 Photos: Donald Trump's rise Trump, center, wears a baseball uniform at the New York Military Academy in 1964. After he graduated from the boarding school, he went to college. He started at Fordham University before transferring and later graduating from the Wharton School, the University of Pennsylvania's business school. Hide Caption 5 of 37 Photos: Donald Trump's rise Trump stands with Alfred Eisenpreis, New York's economic development administrator, in 1976 while they look at a sketch of a new 1,400-room renovation project of the Commodore Hotel. After graduating college in 1968, Trump worked with his father on developments in Queens and Brooklyn before purchasing or building multiple properties in New York and Atlantic City, New Jersey. Those properties included Trump Tower in New York and Trump Plaza and multiple casinos in Atlantic City. Hide Caption 6 of 37 Photos: Donald Trump's rise Trump attends an event to mark the start of construction of the New York Convention Center in 1979. Hide Caption 7 of 37 Photos: Donald Trump's rise Trump wears a hard hat at the Trump Tower construction site in New York in 1980. Hide Caption 8 of 37 Photos: Donald Trump's rise Trump was married to Ivana Zelnicek Trump from 1977 to 1990, when they divorced. They had three children together: Donald Jr., Ivanka and Eric. Hide Caption 9 of 37 Photos: Donald Trump's rise The Trump family, circa 1986. Hide Caption 10 of 37 Photos: Donald Trump's rise Trump uses his personal helicopter to get around New York in 1987. Hide Caption 11 of 37 Photos: Donald Trump's rise Trump stands in the atrium of the Trump Tower. Hide Caption 12 of 37 Photos: Donald Trump's rise Trump attends the opening of his new Atlantic City casino, the Taj Mahal, in 1989. Hide Caption 13 of 37 Photos: Donald Trump's rise Trump signs his second book, "Trump: Surviving at the Top," in 1990. Trump has published at least 16 other books, including "The Art of the Deal" and "The America We Deserve." Hide Caption 14 of 37 Photos: Donald Trump's rise Trump and singer Michael Jackson pose for a photo before traveling to visit Ryan White, a young child with AIDS, in 1990. Hide Caption 15 of 37 Photos: Donald Trump's rise Trump dips his second wife, Marla Maples, after the couple married in a private ceremony in New York in December 1993. The couple divorced in 1999 and had one daughter together, Tiffany. Hide Caption 16 of 37 Photos: Donald Trump's rise Trump putts a golf ball in his New York office in 1998. Hide Caption 17 of 37 Photos: Donald Trump's rise An advertisement for the television show "The Apprentice" hangs at Trump Tower in 2004. The show launched in January of that year. In January 2008, the show returned as "Celebrity Apprentice." Hide Caption 18 of 37 Photos: Donald Trump's rise A 12-inch talking Trump doll is on display at a toy store in New York in September 2004. Hide Caption 19 of 37 Photos: Donald Trump's rise Trump attends a news conference in 2005 that announced the establishment of Trump University. From 2005 until it closed in 2010, Trump University had about 10,000 people sign up for a program that promised success in real estate. Three separate lawsuits -- two class-action suits filed in California and one filed by New York's attorney general -- argued that the program was mired in fraud and deception. Trump's camp rejected the suits' claims as "baseless." And Trump has charged that the New York case against him is politically motivated. Hide Caption 20 of 37 Photos: Donald Trump's rise Trump attends the U.S. Open tennis tournament with his third wife, Melania Knauss-Trump, and their son, Barron, in 2006. Trump and Knauss married in 2005. Hide Caption 21 of 37 Photos: Donald Trump's rise Trump wrestles with "Stone Cold" Steve Austin at WrestleMania in 2007. Trump has close ties with the WWE and its CEO, Vince McMahon. Hide Caption 22 of 37 Photos: Donald Trump's rise For "The Apprentice," Trump was honored with a star on the Hollywood Walk of Fame in January 2007. Hide Caption 23 of 37 Photos: Donald Trump's rise Trump appears on the set of "The Celebrity Apprentice" with two of his children -- Donald Jr. and Ivanka -- in 2009. Hide Caption 24 of 37 Photos: Donald Trump's rise Trump poses with Miss Universe contestants in 2011. Trump had been executive producer of the Miss Universe, Miss USA and Miss Teen USA pageants since 1996. Hide Caption 25 of 37 Photos: Donald Trump's rise In 2012, Trump announces his endorsement of Republican presidential candidate Mitt Romney. Hide Caption 26 of 37 Photos: Donald Trump's rise Trump speaks in Sarasota, Florida, after accepting the Statesman of the Year Award at the Sarasota GOP dinner in August 2012. It was shortly before the Republican National Convention in nearby Tampa. Hide Caption 27 of 37 Photos: Donald Trump's rise Trump appears on stage with singer Nick Jonas and television personality Giuliana Rancic during the 2013 Miss USA pageant. Hide Caption 28 of 37 Photos: Donald Trump's rise In June 2015, during a speech from Trump Tower, Trump announced that he was running for President. He said he would give up "The Apprentice" to run. Hide Caption 29 of 37 Photos: Donald Trump's rise Trump -- flanked by U.S. Sens. Marco Rubio, left, and Ted Cruz -- speaks during a CNN debate in Miami on March 10. Trump dominated the GOP primaries and emerged as the presumptive nominee in May. Hide Caption 30 of 37 Photos: Donald Trump's rise The Trump family poses for a photo in New York in April. Hide Caption 31 of 37 Photos: Donald Trump's rise Trump speaks during a campaign event in Evansville, Indiana, on April 28. After Trump won the Indiana primary, his last two competitors dropped out of the GOP race. Hide Caption 32 of 37 Photos: Donald Trump's rise Trump delivers a speech at the Republican National Convention in July, accepting the party's nomination for President. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people." Hide Caption 33 of 37 Photos: Donald Trump's rise Trump faces Democratic nominee Hillary Clinton in the first presidential debate, which took place in Hempstead, New York, in September. Hide Caption 34 of 37 Photos: Donald Trump's rise Trump apologizes in a video, posted to his Twitter account in October, for vulgar and sexually aggressive remarks he made a decade ago regarding women. "I said it, I was wrong and I apologize," Trump said, referring to lewd comments he made during a previously unaired taping of "Access Hollywood." Multiple Republican leaders rescinded their endorsements of Trump after the footage was released. Hide Caption 35 of 37 Photos: Donald Trump's rise Trump walks on stage with his family after he was declared the election winner on November 9. "Ours was not a campaign, but rather, an incredible and great movement," he told his supporters in New York. Hide Caption 36 of 37 Photos: Donald Trump's rise Trump is joined by his family as he is sworn in as President on January 20. Hide Caption 37 of 37

He said the Iowa state GOP receives 10 to 20 calls per week from rank-and-file Republicans wondering what, specifically, the party will do to force Kasich, Cruz and Bush to stick to their pledges and back Trump.

"If I'm hearing it here from a state of 3 million, it must a megaphone there in DC," said Kaufmann, who has spoken with Priebus and other Republican officials about enforcing the pledge. "There's no wiggle room in terms of what that promise was, and it should be honored."

A representative for Priebus didn't comment on the conversations.

But his call for penalties wasn't widely embraced -- with the No. 2 House Republican breaking with Priebus Tuesday morning.

"There's a better way to unite people. I'm not a big believer that punishment unites people," House Majority Leader Kevin McCarthy told reporters at a weekly session in the Capitol.

The California Republican added, "If Hillary (Clinton) can't unite Republicans, I don't think anything can."

Premature conversation?

Of course, talk of penalties on candidates who might run in 2020 could be all for naught if Trump wins. The race between Trump and Clinton has narrowed dramatically in recent weeks, though the Democratic nominee still has more paths to the White House. But the episode underscores the frenzy that could consume the GOP if Trump loses the race and the party searches for a new direction.

"We're watching the trailer for the GOP civil war, out in theaters November 9," said a top Republican strategist, who asked not to be named to avoid openly feuding with Priebus.

The penalty talk spilled into the open Sunday, when Priebus told John Dickerson on CBS' "Face the Nation" that members of the 2016 Republican presidential field who haven't yet abided by their pledge to back the eventual nominee and endorsed Trump need to "get on board." And for those who don't, he said future presidential bids won't "be that easy."

"If a private entity puts forward a process and has agreement with the participants in that process, and those participants don't follow through with the promises that they made in that process," Priebus said, "what should a private party do about that if those same people come around in four or eight years?"

Kasich's camp quickly zipped off a response accusing Priebus of putting party over principles. Kasich strategist John Weaver said the Ohio governor "will not be bullied by a Kenosha political operative that is unable to stand up for core principles or beliefs."

Photos: The Republican National Convention Photos: The Republican National Convention Donald Trump, the Republican Party's presidential nominee, delivers a speech Thursday at the Republican National Convention in Cleveland. "I have had a truly great life in business," he said. "But now, my sole and exclusive mission is to go to work for our country -- to go to work for you. It's time to deliver a victory for the American people." Hide Caption 1 of 77 Photos: The Republican National Convention Trump is seen on screen as balloons fall from the ceiling of Quicken Loans Arena. Hide Caption 2 of 77 Photos: The Republican National Convention Trump's family joins him on stage along with the family of his running mate, Indiana Gov. Mike Pence. Hide Caption 3 of 77 Photos: The Republican National Convention Confetti falls at the end of Trump's acceptance speech. Hide Caption 4 of 77 Photos: The Republican National Convention Trump and Pence acknowledge the audience after Trump's speech. Hide Caption 5 of 77 Photos: The Republican National Convention Trump claps on stage with his wife, Melania. Hide Caption 6 of 77 Photos: The Republican National Convention The Trumps embrace on stage. Hide Caption 7 of 77 Photos: The Republican National Convention Trump hugs his son Barron after his address, which lasted well over an hour. Hide Caption 8 of 77 Photos: The Republican National Convention Trump, like many of the convention's speakers this week, went after Hillary Clinton, the Democratic Party's presumptive nominee. "Big business, elite media and major donors are lining up behind the campaign of my opponent because they know she will keep our rigged system in place," he said. "They are throwing money at her because they have total control over everything she does. She is their puppet, and they pull the strings." Hide Caption 9 of 77 Photos: The Republican National Convention Trump delivers his speech. Hide Caption 10 of 77 Photos: The Republican National Convention Trump said the United States will be a nation of "generosity and warmth" and "law and order." Hide Caption 11 of 77 Photos: The Republican National Convention A delegate listens to Trump's speech. Hide Caption 12 of 77 Photos: The Republican National Convention "Nobody knows the system better than me, which is why I alone can fix it," Trump said. "My message is that things have to change -- and they have to change right now." Hide Caption 13 of 77 Photos: The Republican National Convention Trump accepts the party's nomination as he begins his speech. Hide Caption 14 of 77 Photos: The Republican National Convention Trump's daughter Ivanka takes the stage Thursday before giving a speech introducing her father. Hide Caption 15 of 77 Photos: The Republican National Convention "This is the moment, and Donald Trump is the person to make America great again!" Ivanka Trump said to a big cheer. She called her father a fighter, saying now he will "fight for his country." Hide Caption 16 of 77 Photos: The Republican National Convention Peter Thiel, co-founder of PayPal, became the first openly gay person to speak the Republican National Convention. "I am proud to be gay," he told the crowd Thursday. "I am proud to be a Republican. But most of all I am proud to be an American." Hide Caption 17 of 77 Photos: The Republican National Convention Reince Priebus, chairman of the Republican National Committee, delivers a speech on Thursday. "We are the party of new ideas in a changing and faster world than ever before," he said. Hide Caption 18 of 77 Photos: The Republican National Convention Legendary basketball coach Bob Knight delivers a video message to the crowd at Quicken Loans Arena. Hide Caption 19 of 77 Photos: The Republican National Convention Motivational speaker Brock Mealer was among those who spoke on Thursday. Hide Caption 20 of 77 Photos: The Republican National Convention A delegate dressed as Hillary Clinton is accosted by another delegate on Thursday. Hide Caption 21 of 77 Photos: The Republican National Convention Delegates stand for the national anthem Thursday. Hide Caption 22 of 77 Photos: The Republican National Convention Young singer Heavenly Joy performs. Hide Caption 23 of 77 Photos: The Republican National Convention Trump gives a thumbs-up Wednesday after Pence gave his speech. Hide Caption 24 of 77 Photos: The Republican National Convention Trump gives an "air kiss" to Pence after Pence's speech. Hide Caption 25 of 77 Photos: The Republican National Convention Pence receives a kiss from his mother, Nancy, as his family joins him on stage after his speech. Hide Caption 26 of 77 Photos: The Republican National Convention Pence acknowledges the crowd as he walks on stage to deliver his speech. Hide Caption 27 of 77 Photos: The Republican National Convention "I'm a Christian, a conservative and a Republican, in that order," Pence told the crowd. Hide Caption 28 of 77 Photos: The Republican National Convention Former House Speaker Newt Gingrich delivers a speech on Wednesday. Hide Caption 29 of 77 Photos: The Republican National Convention Trump smiles on the floor of the convention on Wednesday. Hide Caption 30 of 77 Photos: The Republican National Convention Eric Trump, one of Donald Trump's sons, walks on stage to deliver a speech Wednesday. Hide Caption 31 of 77 Photos: The Republican National Convention Trump listens to his son's speech along with other members of his family on Wednesday. Hide Caption 32 of 77 Photos: The Republican National Convention Delegates shout on the floor of the arena on Wednesday. Hide Caption 33 of 77 Photos: The Republican National Convention U.S. Sen. Ted Cruz, Trump's main adversary in the primaries, was booed at the end of his speech when it was clear he wasn't endorsing Trump. Cruz told people to "vote your conscience." Hide Caption 34 of 77 Photos: The Republican National Convention People react to Cruz's speech. Hide Caption 35 of 77 Photos: The Republican National Convention Cruz gives a thumbs-up as he walks off stage. Hide Caption 36 of 77 Photos: The Republican National Convention U.S. Sen. Marco Rubio, another one of Trump's primary opponents, delivers a video message. Hide Caption 37 of 77 Photos: The Republican National Convention A delegate checks his phone at the arena. Hide Caption 38 of 77 Photos: The Republican National Convention Wisconsin Gov. Scott Walker delivers a speech Wednesday. "A vote for anyone other than Donald Trump in November is a vote for Hillary Clinton," the former presidential candidate said. Hide Caption 39 of 77 Photos: The Republican National Convention Delegates hold up signs Wednesday. Hide Caption 40 of 77 Photos: The Republican National Convention Retired astronaut Eileen Collins waves to the crowd before delivering a speech Wednesday. Hide Caption 41 of 77 Photos: The Republican National Convention Trump addresses the crowd on Tuesday. "We're going to make America great again," he said in a video message shortly after winning the nomination. "Have a fantastic evening. I'll see you tomorrow night, I'll see you Thursday night, and we will win in November." Hide Caption 42 of 77 Photos: The Republican National Convention Ben Carson, a retired neurosurgeon and former presidential candidate, speaks on stage Tuesday. He said Trump skeptics who would vote for Hillary Clinton are "not using their God-given brain to think about what they're saying. ... She'll be appointing people who will have an effect on us for generations. And America may never recover." Hide Caption 43 of 77 Photos: The Republican National Convention A member of the activist group Code Pink protests inside the arena during Carson's speech. Hide Caption 44 of 77 Photos: The Republican National Convention Donald Trump Jr. delivers a speech Tuesday. "We need to elect a man who has a track record of accomplishing the impossible," he said of his father. Hide Caption 45 of 77 Photos: The Republican National Convention Members of the Trump family watch as Donald Trump Jr. gives his speech. Hide Caption 46 of 77 Photos: The Republican National Convention Donald Trump's daughter Tiffany addresses the crowd at Quicken Loans Arena. "Whatever (my father) does, he gives it all and does it well," she said on Tuesday. "His desire for excellence is contagious. He possesses a unique gift for bringing that out in others." Hide Caption 47 of 77 Photos: The Republican National Convention U.S. Sen. Joni Ernst waves as she stands with other first-term senators on Tuesday. Hide Caption 48 of 77 Photos: The Republican National Convention New Jersey Gov. Chris Christie delivers a speech that was heavily critical of the Democratic Party's presumptive nominee. "It is our obligation to stop Hillary Clinton now and never let her within 10 miles of the White House again," Christie said of the former secretary of state. "It is time to come together and make sure that Donald Trump is our next President. I am proud to be part of this team. Now let's go win this thing." Hide Caption 49 of 77 Photos: The Republican National Convention Delegates fill the floor of the arena on Tuesday. Hide Caption 50 of 77 Photos: The Republican National Convention Four of Donald Trump's children -- from left, Donald Trump Jr., Ivanka Trump, Eric Trump and Tiffany Trump -- celebrate on the floor of the convention, where Donald Trump Jr. announced the New York delegates that clinched the nomination for his father. Hide Caption 51 of 77 Photos: The Republican National Convention A delegate shows support for Donald Trump's wife, Melania, on Tuesday. Hide Caption 52 of 77 Photos: The Republican National Convention A delegate whistles as roll call votes are cast on Tuesday. Hide Caption 53 of 77 Photos: The Republican National Convention Delegates take a photo with Mississippi Gov. Phil Bryant, center, on Tuesday. Hide Caption 54 of 77 Photos: The Republican National Convention A Florida delegate holds a "Hillary for prison" sign on the floor of the arena. Hide Caption 55 of 77 Photos: The Republican National Convention A convention attendee wears American-themed shoes on Tuesday. Hide Caption 56 of 77 Photos: The Republican National Convention House Speaker Paul Ryan bangs the gavel to open the second day of the convention on Tuesday. Hide Caption 57 of 77 Photos: The Republican National Convention Melania Trump kisses her husband, Donald, after she spoke Monday on the first day of the convention. "If you want someone to fight for you and your country, I can assure you, he's the guy," she said of her husband. "He will never, ever give up. And most importantly, he will never, ever let you down." Hide Caption 58 of 77 Photos: The Republican National Convention Donald Trump walks to his wife after she delivered her speech. Hide Caption 59 of 77 Photos: The Republican National Convention Melania Trump claps during her speech. Hide Caption 60 of 77 Photos: The Republican National Convention Donald Trump comes out to the song "We Are the Champions" before introducing his wife. Hide Caption 61 of 77 Photos: The Republican National Convention Former New York City Mayor Rudy Giuliani delivered a fiery speech before Melania Trump. Among his topics was the fight against terrorists. "We know who you are, and we're coming to get you!" he said. Hide Caption 62 of 77 Photos: The Republican National Convention A protester flashes a peace sign on the floor of the convention on Monday. Hide Caption 63 of 77 Photos: The Republican National Convention Milwaukee County Sheriff David A. Clarke Jr. salutes the crowd before speaking Monday. He got huge applause when he started off his speech by saying, "Blue lives matter!" Hide Caption 64 of 77 Photos: The Republican National Convention Patricia Smith, mother of Benghazi victim Sean Smith, told the crowd in Cleveland, "I blame Hillary Clinton personally." Clinton, the Democratic Party's presumptive nominee, was secretary of state when the attack occurred in Libya in 2012. Hide Caption 65 of 77 Photos: The Republican National Convention President Barack Obama is seen on a screen as Smith leaves the stage Monday. Hide Caption 66 of 77 Photos: The Republican National Convention Marcus Luttrell, a former Navy SEAL who was awarded the Navy Cross for his service in Afghanistan, spoke about the need for an elite military. The convention's theme for Monday was "Make America Safe Again." Hide Caption 67 of 77 Photos: The Republican National Convention Actor Scott Baio gives two thumbs up during his speech on Monday. "Let's not just make America great again," he said, referring to Trump's campaign slogan. "Let's make America America again!" Hide Caption 68 of 77 Photos: The Republican National Convention Willie Robertson, star of the hit TV show "Duck Dynasty," promised the crowd that Trump "will have your back." Hide Caption 69 of 77 Photos: The Republican National Convention Former U.S. Sen. Bob Dole, the GOP's presidential nominee in 1996, waves after listening to a speech on Monday. Hide Caption 70 of 77 Photos: The Republican National Convention Marlana VanHoose performs the national anthem prior to Monday's evening session. Hide Caption 71 of 77 Photos: The Republican National Convention Former Virginia Attorney General Ken Cuccinelli, center, was among the delegates shouting for a roll call vote Monday on the rules of the Republican National Convention. GOP officials dismissed the move, saying there were not enough signatures to force a roll call vote. While it's unlikely a roll call vote would have rejected the rules package, it could have been an embarrassing protest vote against Trump and the Republican National Committee. Hide Caption 72 of 77 Photos: The Republican National Convention Virginia delegate Waverly Woods protests on the floor of the convention. Hide Caption 73 of 77 Photos: The Republican National Convention Delegates from Texas protest. Hide Caption 74 of 77 Photos: The Republican National Convention Reince Priebus, chairman of the Republican National Committee, bangs a gavel as resolutions are adopted at the start of the convention. Hide Caption 75 of 77 Photos: The Republican National Convention Delegates stand and turn toward the camera for an official photo on Monday. Hide Caption 76 of 77 Photos: The Republican National Convention People walk in front of a screen displaying the American flag. Hide Caption 77 of 77

Cruz brushed Priebus off Tuesday evening.

"These are serious times. I think the last thing we need to worrying about is bickering between Republicans," he said. "My focus is on defeating Hillary Clinton and helping preserve a Senate Republican majority."

The RNC's leverage

Penalties, several Republicans said, would likely come from the national party in the form of restrictions on access to the Republican National Committee's data and voter files -- and potentially bans from primary debates. Individual states, though, likely couldn't keep candidates off their ballots.

Still, Republicans cautioned that talk of penalizing pledge-breakers is aimed at nudging Kasich, Cruz, Bush and others to support Trump in 2016 -- not to handicap the party's presidential candidates in the future. Some said it's not even clear the RNC would have authority to impose the crackdown Priebus discussed.

"Reince has simply posed a question to which there is no good answer yet -- and I'm not sure that the question deserves an answer. That's to be determined," said Matt Moore, the South Carolina GOP chairman.

RNC spokeswoman Lindsay Walters declined to address the possibility of penalizing future presidential candidates who didn't abide by their pledges to support Trump.

"We are focused on winning back the White House and maintaining our majorities in the House and Senate," Walters said in an email.

While some party honchos like Kaufmann backed Priebus' warning shot, others -- including Ohio GOP chairman Matt Borges -- bristled.

"No. This is not what we are all about as a party. Besides, let's stay focused on 2016 for the next 50 days," Borges tweeted Sunday night.

Top Mitt Romney 2012 strategist Stuart Stevens tweeted: "So idea is most popular recent Republican governors of battleground states should run as independents? Great plan."

RNC's handling of Trump

The RNC's handling of Trump under Priebus will be on trial as the party picks a new chair -- or extends the Wisconsin operative's tenure -- shortly after the election. Then comes a swing-state governor's race in Virginia, followed by the midterm elections, where Trump's brand of populism could butt against more orthodox conservatives.

And in 2020, the early stages of the Republican primary would be defined by how the candidates treated Trump. It would be the clearest differentiator of like-minded conservatives like Mike Pence, the Indiana governor who became Trump's running mate and chief defender, and Cruz, the Texas senator who was booed off stage for refusing to endorse Trump at his own nominating convention.

"Assuming Trump loses, there'll be a really pitched battle for the heart and soul of the party," said Weaver, the Kasich strategist who wrote the scathing rebuttal to Priebus on Sunday.

"You're going to have off-year elections, you're going to have midterms -- some of that will impact the defining of the party, clearly. But you won't have any new definition of it until there's a new nominee," Weaver said. "There's a broader debate ultimately about what the party stands for and where the country should go."

Many Republicans still fault Priebus for failing to criticize Trump forcefully enough in late 2015, when he proposed a clearly unconstitutional ban of all Muslims from entering the United States, and believe the party could have done more to slow Trump's rise.

They point out a particular irony: The party that insisted it couldn't intercede in the 2016 nominating contest is now threatening to use its leverage to undercut individual candidates in future races.

Saul Anuzis, a former Michigan GOP chairman who helmed Cruz's state effort in the primary, defended pledge-breaking candidates, arguing that "circumstances change" -- a reference to the pledge's creation as a tool to keep Trump from launching an independent campaign.

He said he doesn't see how Priebus could impose penalties on future presidential candidates.

"There's no provisions in the RNC rules that allow anybody to punish anybody," Anuzis said. "The idea of doing that, I think, is extremely difficult, because you normally are looking toward the future, not the past."