ATLANTA — Democratic Party insiders say efforts to draft Sen. Bernard Sanders to launch a political party are foolish, doomed to fail and could do more to hurt than help the progressive cause.

The pressure on Mr. Sanders to strike out on his own is intensifying now that former Labor Secretary Tom Perez was elected chairman of the Democratic National Committee, overcoming a stiff challenge from Rep. Keith Ellison and progressive activists who say the party’s primary race last year was rigged against the Vermont independent.

But DNC members gathered here said the efforts — including from the Draft Bernie for a People’s Party — are misguided.

“He ran for president through the party, did extraordinarily well, better than anybody thought he was going to do, and I think it is incumbent upon him to make sure that his base stays in line with the party to ensure that we win races,” said Daniel Halpern, a DNC member from Georgia.

Whether Mr. Sanders can control the movement he launched is another question. Pro-Sanders progressives may have nothing in common ideologically with the tea party, but they are poised to wreak the same kind of intraparty havoc by taking on the Democratic establishment in 2018 — or sooner.

Democrats facing re-election next year already are hearing buzz around primary challenges from the left as progressives move to flush out the establishment and put their stamp on the party, just as the tea party did on the Republican Party in 2010 and 2012.

Democratic activists have formed #WeWillReplaceYou to threaten incumbents with primary challengers if they fail to tow the anti-Trump line by voting against the president at every opportunity. They are warning that “Democrats must know there is a price for collaborating with Trump.”

Adam Green, co-founder of the Progressive Change Campaign Committee, threw down the gauntlet before the DNC chairmanship race by saying that “ideally there would be no need for primaries against incumbents because Democrats in office will fight Trump so boldly, consistently and effectively.”

“But to be clear: Democratic politicians in red states who fail to fight strongly against Trump and seize the mantle of economic populism won’t inspire people to vote — and they will lose the general election in 2018,” Mr. Green said.

The uprising has begun on a local level. The party leadership and Democratic central committees are more progressive than ever after Sanders voters in some states flooded caucuses and in some cases ousted the so-called establishment.

If the Republican Party’s 11th commandment is “never speak ill of another Republican,” as President Reagan advised, then the Democratic Party’s unofficial mantra for years has been to avoid primary challenges against shaky incumbents at all costs.

But that’s changing.

Sen. Claire McCaskill, Missouri Democrat, acknowledged that she could be among the progressives’ top targets in the primary next year.

“I am for sure going to run, and I may have a primary because there is in our party now some of the same kind of enthusiasm at the base that the Republican Party had with the tea party,” Ms. McCaskill told KMOX-AM in St. Louis host Mike Reardon last week. “And many of those people are very impatient with me because they don’t think I’m pure.”

Other Senate Democrats ripe for a progressive primary challenge include Joe Donnelly of Indiana, Heidi Heitkamp of North Dakota, Joe Manchin III of West Virginia and Jon Tester of Montana.

The problem for the party? Those Democrats all represent states won by President Trump, who was elected by voters who may not feel, as the progressive resistance does, that the relatively moderate incumbents aren’t far enough to the left.

“In terms of pure tactics, if they do primaries to get the most liberal candidates possible in states where Democrats are vulnerable or where they have a chance, it would be just suicidal,” said political consultant Floyd Ciruli. “They need three states to take the Senate. They’ll be lucky if they don’t lose three states if the strategy turns out to be, ‘Give primaries to vulnerable incumbents.’”

Democrats have scrambled to head off a tea party redux by reaching out to the progressive upstarts. Mr. Perez set the tone Sunday by quickly naming his opponent, Mr. Ellison of Minnesota, as his deputy chairman.

Both urged party unity after Saturday’s vote, but Ellison supporters weren’t necessarily ready to hear it, chanting, “Party for the people! Not big money!”

“If people trust me, then they need to come on and trust Tom Perez as well,” Mr. Ellison told the crowd.

Even though Mr. Ellison lost, the vote proved that the upstarts have the passion and the numbers. The final tally was 235-200 in favor of Mr. Perez, who had the support of the party’s powerful Obama and Clinton camps.

Sanders ally Jim Zogby, a DNC member from the District of Columbia, said Mr. Sanders is absolutely better off trying to channel his popularity and the activist energy that has sprouted up against Mr. Trump into transforming the Democratic Party from the inside.

“You only create alternative institutions when an institution is not capable of absorbing your energy or making change,” Mr. Zogby said.

“We have taken over several states since the election,” Mr. Zogby said. “I think we can do more. This is not a six-month battle. It is multiyear battle, and my sense is this Democratic Party will be a very different party four years from now than it is today.”

But leaders of the Draft Bernie for a People’s Party ditched the Democrats after the November election, arguing that the leaders of the DNC — first Rep. Debbie Wasserman Schultz and then Donna Brazile — helped rig the primary in favor of Mrs. Clinton.

Mr. Ellison’s loss, and the DNC’s decision to shoot down a resolution calling for a ban on corporate donations, showed that they are in need of a new affiliation.

“There is no future for progressives in the Democratic Party,” the group said in a statement.

The group envisions fielding a presidential candidate in 2020 and running candidates in 2018 against Republicans in districts where Mr. Sanders‘ populist message could resonate, as well as against Democrats in blue districts that supported Mr. Sanders in the presidential primary.

Asked about the People’s Party push, Jeff Weaver, a longtime adviser to Mr. Sanders, said, “I don’t know if that one is that serious.”

But he acknowledged that Mr. Sanders “has not closed the door” on a third-party run.

“I don’t know that he would run outside the party,” Mr. Weaver said of a second presidential bid. “I think he would run in the Democratic primaries like he did in 2016.”

John Graham, a DNC member from New Jersey, predicted the party would prevail.

“I see that you have to work within the structure to make it better because whenever something becomes too radical left or too radical right, it falls apart,” Mr. Graham said.

He added, “Bernie likes the attention too.”

Mark Hammond, chairman of the Oklahoma Democratic Party, said he hopes Mr. Sanders sticks with the party.

“Third parties have never been successful,” Mr. Hammond said. “This has always been a two-party country from its inception. No third party has lasted long.

“The impact of a Bernie’s People Party or a populist party would be to split the progressive vote into two components and ensure a pretty regressive Republican control,” he said. “They would be spoilers. To a degree, the ‘Bernie or Bust’ people were spoilers.”

• Seth McLaughlin reported from Atlanta. Valerie Richardson is in Colorado.

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