Less than 24 hours after President Barack Obama aimed to set the tone for the country on a response to the threat of terrorism with an Oval Office address, Trump only needed a press release to cause an uproar with his call for an outright ban on Muslims entering the United States

The billionaire businessman stood defiantly by his statement on Tuesday morning, when he warned that failing to follow his plans would lead to another September 11-style terror attack on U.S. soil.

"You're going to have many more World Trade Centers if you don't solve it -- many, many more and probably beyond the World Trade Center," Trump told CNN's Chris Cuomo in a contentious interview on "New Day."

The episode is a microcosm of how the 2016 campaign has played out. Trump has consistently forced candidates, state party chairs, senators and conservative pundits to respond to his actions and quotes, however outlandish and improbable. And in turn, they have all struggled with the question of how to deal with the bombastic real estate tycoon who has dominated state and national polls since the summer.

Trump's enduring ability to frame the terms of the debate for the GOP continues to have party leaders fretting he will drive voters to Hillary Clinton, help down-ballot Democrats and cause long-term damage to the Republican brand.

JUST WATCHED Donald Trump defends Muslim ban proposal on CNN's New Day Replay More Videos ... MUST WATCH Donald Trump defends Muslim ban proposal on CNN's New Day 01:09

Yet, unlike with past provocative statements, Trump appears to have sparked a level of backlash from GOP party leaders and his opponents that could be a tipping point for the willingness of fellow Republicans to criticize him directly and openly. Jeb Bush called Trump "unhinged." Ted Cruz said it wasn't his policy. And Dick Cheney, who previously said he would back the Republican nominee even it was Trump, said that Monday's proposal "goes against everything we stand for and believe in."

At a press conference on Tuesday, House Speaker Paul Ryan also slammed Trump.

"This is not conservatism," he said. "What was proposed yesterday is not what this party stands for."

But Trump has been here before -- his blustery statements only seem to have deepened his appeal to a subset of Republican voters, leading to a frustrated party establishment. Predictions of his demise have all proved to be premature.

Still, in an unprecedented move, the state party chairs of the three early presidential contests all waded into the fray, criticizing Trump's idea, suggesting at the very least that Trump has crossed a line they feel could damage the Republican brand.

"After Obama's terrible speech, GOP should be focused on Obama/Clinton foreign policy failures," Jeff Kaufmann, Iowa's GOP chairman, tweeted . "Instead I'm here to reiterate that our founding principles are stronger than political cynicism," he added

Republican National Committee Chairman Reince Priebus on Tuesday also criticized Trump. "I don't agree," Priebus told the Washington Examiner . "We need to aggressively take on radical Islamic terrorism but not at the expense of our American values."

According to a CNN/ORC poll released Monday , Trump leads his GOP opponents by double digits in Iowa, garnering support from 33% of likely Republican caucus-goers, with Ted Cruz in second at 20%.

"As a conservative who truly cares about religious liberty, Donald Trump's bad idea and rhetoric send a shiver down my spine," South Carolina GOP chairman Matt Moore tweeted. "American exceptionalism means always defending our inalienable rights, not attacking them when it's politically convenient."

Moore did not answer a follow-up question about whether he thinks Trump's comments are disqualifying and whether he would back him if he wins the nomination.

(1/2) As a conservative who truly cares about religious liberty, Donald Trump's bad idea and rhetoric send a shiver down my spine. — Matt Moore (@MattMooreSC) December 8, 2015

Trump's proposal, the latest in a string of provocative comments coming in the wake of the terrorist shooting that left 14 dead and 17 wounded in San Bernardino, California, drew cheers and applause from a crowd Monday in Charleston, South Carolina.

"Donald J. Trump is calling for a total and complete shutdown of Muslims entering the United States until our country's representatives can figure out what the hell is going on," said Trump reading from a statement his campaign sent out shortly before the rally. "We have no choice. We have no choice."

Reggie Johnson, 38, who attended Trump's Charleston rally, agreed with the GOP frontrunner.

"I think it should be shut down for now until you find something, a better program in place," he said. "I mean this is a free country for what's that's worth but I think it does need to be shut down until they get a cap on things."

JUST WATCHED Supporters at Trump rally cheer his Muslim travel ban proposal Replay More Videos ... MUST WATCH Supporters at Trump rally cheer his Muslim travel ban proposal 02:22

Commanding the spotlight

Republicans spent Sunday night condemning Obama's speech and his approach to combating terrorism. And they spent Monday night talking about Trump, who called for a religious test for who is admitted to the country right after Obama said it was "our responsibility to reject" such a test.

Bush's super PAC, Right to Rise, will begin running an ad called "Desk" in Iowa, New Hampshire, South Carolina and Nevada, that calls Trump "impulsive and reckless." While the ad doesn't specifically mention Trump's proposal, Bush supporters think he is best positioned to benefit from the shift to national security issues.

JUST WATCHED Graham: Trump is a 'race-baiting, xenophobic' bigot Replay More Videos ... MUST WATCH Graham: Trump is a 'race-baiting, xenophobic' bigot 03:34

"Twenty-seven generals and admirals support Jeb Bush," the ad states. "Because Jeb has the experience and knowledge to protect your family."

Doug Heye, a veteran GOP strategist and former adviser to the Iowa Republican Party, said Trump's latest proposal would do more damage than some of his previous controversial comments.

"There are going to be newspapers throughout the world that are going to read 'Republican front-runner doesn't want Muslims to visit America," said Heye. "It will make it easier for Democrats to portray the GOP as hostile to any minority. Ultimately, I think Donald Trump is the best asset Hillary Clinton has."

Clinton tweeted that Trump's proposal was "reprehensible, prejudiced and divisive." Huma Abedin, Clinton's campaign vice-chairwoman, sent out an e-mail to Clinton supporters with the subject matter -- "I'm a proud Muslim."

"Unfortunately, Trump is leaning into the kind of fear of progress that very well could help him win the nomination," Abedin wrote. "We have to be ready to stop him."

Heye encouraged GOP contenders to condemn Trump's remarks, suggesting they take a dismissive tone like Bush did on Twitter. He warned that Trump's comments would be used to weaken the Republican nominee --- even if it's not Trump -- and will create challenges for Republicans in down-ballot races.

"Everything about Donald Trump's campaign has hurt the Party," Heye said. "It hurts the party on a presidential level. It certainly hurts the party on a Senate level as well."

Senators grapple with Trump phenomenon

Heye's remarks run counter to a strategy revealed in a leaked National Republican Senatorial Committee that suggested one way to run with Trump at the top of the ticket is to adopt his issues, if not his tone and rhetoric.

Senators were all over the map Monday as they were asked about Trump's proposal. Some were happy to blast the GOP front-runner, others, like Iowa's Joni Ernst, wanted nothing to do with the question.

Ernst, who occupies an influential spot among Iowa Republicans walked away from repeated questions about whether she supported Trump's call.

"Oh, I'm not going to comment on that," she said when asked by CNN about his comments. Asked again, she replied: "I am not commenting on him."

South Carolina Sen. Tim Scott, a first-term senator who has been hosting Republican candidates at forums and will be on the ballot in 2016, suggested that Trump's latest statements were simply par for the course.

"A lot of hyperbolic language is used during campaign season," Scott said in a statement to CNN. "We need to focus on serious solutions to address the real dangers presented by ISIS."

Sen. Jeff Sessions, an Alabama Republican who has advised Trump on immigration policy and appeared onstage with him at a rally in Alabama, didn't want to weigh in.

"I've been pleased that he took a lot of my ideas in his immigration policy, but I have not endorsed Mr. Trump or anyone else," Sessions said when asked about Trump's comments. Pressed on whether he would support Trump's proposal, Session's became quiet and stopped talking as he rushed to a Senate elevator.

Sen. Jim Inhofe, an Oklahoma Republican, said that Trump was wrong to call for a ban on all Muslim travel to the U.S. "If he had changed instead of saying Muslim and said radical Islam, then I would agree with him. But I don't agree," Inhofe said, noting that there's a big difference between banning travel for anyone identified as a "radical Islamic terrorist" and all Muslims.

Sen. John McCain, the party's 2008 nominee and a supporter of Sen. Lindsey Graham's long-shot bid was clear: "It's just foolishness. It's been a long series of statements like this that have been just foolish."

McCain and Graham have been among the most critical of Trump, but all to no avail. Graham, for instance, trails Trump in his home state of South Carolina. And when Trump seemed to suggest that McCain, a Vietnam-era POW and the GOP's 2008 nominee, was not a war hero, it didn't hurt his standing in the polls.

RNC caught in difficult spot

Opponents and party leaders seem to be in search of a referee who can credibly rebuke Trump and block his path to the nomination.

"Is the RNC still moving forward with a fundraiser featuring Trump? Asking for a nation...." tweeted John Weaver, a John Kasich adviser.

According to Sean Spicer, a spokesman for the RNC, Trump won't be at a Wednesday fundraiser in New York. But that decision was made well before Trump's latest comments, according to Spicer. Spicer didn't respond to e-mails about Trump's comments about Muslims.

Nervous about what a third party Trump bid would do to the party's general election chances, the RNC moved to officially bring Trump into the GOP tent. He publicly signed a pledge saying that he would run as a Republican at the RNC's urging. Yet his entire campaign has been a rejection of the RNC's rebranding efforts.

We need a leader that will unite us, not divide us @realDonaldTrump - Sign if you agree https://t.co/cdx5VrKtMt pic.twitter.com/G9F2XBMQDF — John Kasich (@JohnKasich) December 8, 2015

In a 2013 autopsy, the RNC argued that to become a winning party at the presidential level, the party must be a more welcoming party and "stop talking to itself." But like no other candidate, Trump knows his audience, repeatedly doubling down on statements that have brought criticism from party elders.

His success highlights the competing factions of a leaderless party, searching for an identity. Republicans sought to strip the conservative label from Trump --- New Hampshire GOP leader Jennifer Horn, called his ideas "un-Republican."

Cheney weighed in as well.

"I think this whole notion that somehow we can just say no more Muslims, just ban a whole religion, goes against everything we stand for and believe in," he said on Hugh Hewitt's radio show. "I mean, religious freedom has been a very important part of our history and where we came from."

Bill Kristol, who tweeted that he has come to loathe Trump for "soiling the robe of conservatism and dragging it through the dust," said in an email to CNN that the RNC is "pretty helpless in situations like this."

But with Trump's latest comments, he said that the stakes are now higher on Trump's opponents, who by now have plenty of practice in criticizing him.