“People in Washington in the political establishment who think we’ll get rid of Trump and go back to normal have made a terrible miscalculation. That’s not going to happen,” said Patrick Caddell, a political strategist who has worked for Democrats for most of his career and has warned that a breakup of the Republican Party is only a matter of time.

“The paradigm shift that we went through in 2016, it’s still in motion,” Mr. Caddell added.

Even with his historically low approval ratings, Mr. Trump is redefining what it means to be a loyal Republican. His antagonism, born of frustration over his stalled agenda, of the top two Republicans in Congress, Speaker Paul D. Ryan and Senator Mitch McConnell, the majority leader, is exacerbating the rifts between leadership-friendly Republicans and more anti-establishment renegades.

“Before Trump, I saw the ongoing battle between what I would call the pragmatic governing wing and the purists — that was the litmus test issue,” said Representative Charlie Dent, a Pennsylvania Republican who announced last week that he was retiring, in part because he was fed up with the gridlock and infighting in Congress.

“Now, since Trump,” Mr. Dent added, “the issue has become, more or less, Trump loyalty.”

Representative Dave Brat, the Virginia Republican who unseated Eric Cantor, the No. 2 House Republican, in 2014, said the rise of anti-establishment figures like Mr. Trump on the right and Senator Bernie Sanders on the left showed the desire for disruption in both parties. But that disruption has been slow going in Congress, much to the irritation of voters who have little loyalty to the Democratic or Republican brands.

“That is the new movement — Bernie through Trump,” Mr. Brat said. “It hasn’t permeated Congress, and that’s why everybody is ticked.”

For all practical purposes, neither Mr. Ryan nor Mr. McConnell has a functioning majority they can count on to pass legislation, as has been vividly illustrated by the failure to fulfill longstanding vows to repeal the Affordable Care Act. And Republicans said they expected that opposition to party leaders would become the new test for candidates in the primary fights before the 2018 midterm elections.