Mr. Straus’s dash for the exits followed the retirement announcements of Mr. Flake, Senator Bob Corker of Tennessee and Representatives Ileana Ros-Lehtinen of Florida, Charlie Dent of Pennsylvania, Pat Tiberi of Ohio and Dave Reichert of Washington State — all members of the Republican establishment.
Many of those who remain will have to accommodate the president to survive primaries from the pro-Trump right. Already, in the high-profile campaigns of 2017 — governor races in Virginia and New Jersey and a special Senate race in Alabama — Republican candidates are mirroring Mr. Trump’s racially tinged campaign tactics. And Republican officials are putting up with the sort of incendiary candidacy that a party more devoted to nurturing a tolerant image might have rejected.
“We’re not an element,” said Laura Ingraham, a pro-Trump talk show host. “We’re the party.”
Ms. Ingraham, the author of a new book, “Billionaire at the Barricades,” on the populist uprising that helped elect Mr. Trump, said the conservatism of market-oriented internationalism simply has little mass appeal.
“There’s no constituency for open borders, endless war and these international trade deals that are skewed against the United States,” she said.
As for the limited government pitch that defined Mr. Flake’s career, Stephen K. Bannon, the president’s former chief strategist, scoffed.
“This thing they’ve got today doesn’t work, it doesn’t move with urgency,” said Mr. Bannon, who is now orchestrating an effort to defeat Republicans deemed insufficiently loyal to Mr. Trump’s agenda. “It’s very nice. But it’s a theoretical exercise. It can’t win national elections.”
Even some of the president’s detractors on the right believe that the party base will stick with him because they like his agenda.
“We have a leader who has a personality disorder,” said former Senator Tom Coburn, Republican of Oklahoma, “but he’s done what he actually told the people he was going to do, and they’re not going to abandon him.”
This grass-roots loyalty is why no prominent Republicans on the ballot next year have broken with Mr. Trump — only lame-duck lawmakers and Republicans out of office, such as former President George W. Bush, have been harshly critical of him.
At the moment, congressional Republicans and Mr. Trump are trying to make common cause of an overhaul of the tax code because they see it as something of a temporary cure-all. A bill-signing ceremony on taxes would hand lawmakers something to run on next year and the president a much-needed accomplishment.
“It stops the bleeding,” said Senator Lindsey Graham, of South Carolina.
But even that holds risks. A tax cut that skews heavily toward corporations and the rich would hardly dislodge the populist view of a Republican establishment beholden to its donors.
“I don’t think the rank-and-file Republican believes that corporations are people,” said Sam Nunberg, a former adviser to the Trump campaign who has also worked with Mr. Bannon. He was mimicking a Mitt Romney quote that earned Mr. Romney, the 2012 Republican presidential nominee, ridicule for being out of touch.
“We have, actually, great unity in the Republican Party,” he told reporters before leaving for a fund-raiser in Texas.
But even as Mr. Trump won repeated standing ovations from Senate Republicans on Tuesday when he visited their weekly lunch at the Capitol, the party’s lingering tensions were also on display. Senator Pat Roberts of Kansas, a longtime member of the Agriculture Committee, expressed concern about whether Mr. Trump would pull out of the North American Free Trade Agreement, according to a Republican present at the luncheon.
Less than an hour after Mr. Trump left the Capitol, Mr. Flake was on the Senate floor delivering a 17-minute excoriation of the Trump era.
How aggressively the president pursues his platform on trade and immigration restrictionism could test how strong his grip is on Congress.
For now, though, the vision for a more populist-nationalist party sketched out by Mr. Bannon is being won as much through intimidation as through actual purges in Republican primaries.
What Mr. Bannon is trying to do — and what Mr. Flake’s retirement could further — is strike fear in the hearts of Republicans who do not display enough enthusiasm for the nationalism that Mr. Trump ran on.
“This should be a warning shot to any other ‘Never Trumper’ in the Senate today: Your time is up,” Mr. Surabian said.
That is playing out not only in the examples of Mr. Flake and Mr. Corker.
In Nevada and Mississippi, Senators Dean Heller and Roger Wicker have responded to Trump-inspired primary threats by taking steps to emphasize their fealty to Mr. Trump.
On Wednesday, Senator John Cornyn of Texas, the No. 2 Republican in the Senate, endorsed former Judge Roy S. Moore in the Alabama Senate race, praising Mr. Moore, a caustic social conservative, as “a tireless advocate led by principle rather than politics.” Mr. Cornyn is the highest ranking Republican to formally back Mr. Moore.
But accommodation is not giving pause to would-be rivals. Danny Tarkanian, Mr. Heller’s Republican challenger, said the conversation among activists was no longer dominated by finding the most conservative candidates.
“The talk I hear is, ‘Hey, who’s going to support Trump’s “America First” policies,’” said Mr. Tarkanian, citing trade, military intervention and what he described as “worrying more about refugees from other countries than our own people.”
In the House, some lawmakers who have previously spoken out against Mr. Trump, such as Representative Martha Roby, Republican of Alabama, are now working to repair their relationship with the White House.
“The message they’re sending is: The way to survive is by accommodating him, changing their tone and professing loyalty to Trump,” said William Kristol, the former editor of The Weekly Standard and a vociferous Trump critic.
The two governor’s races this year also illustrate Mr. Trump’s influence in the party. In Virginia and New Jersey, the establishment-aligned Republican nominees for governor, Ed Gillespie and Kim Guadagno, are airing controversial ads on immigration to both stir their base and win over some independents concerned about crimes committed by those in the country illegally. Mr. Gillespie, a veteran Washington lobbyist who served in George W. Bush’s White House, is also running ads extolling his support for Confederate statues.
In the Senate, Republicans have made clear that they will welcome Mr. Moore of Alabama — who has a decades-long history of making inflammatory comments about gays, African-Americans and Muslims — to their ranks should he win the special election in December to fill the seat left vacant by Jeff Sessions, now the attorney general. A handful of conservative writers have expressed concern about the message that tolerating Mr. Moore sends, but no high-profile lawmaker has followed suit, and a pair of Republican senators are even hosting a fund-raiser for him next month in Washington.
And in Colorado, former Representative Tom Tancredo, who was shunned by the Bush-era Republican Party for his harsh anti-immigration views, is considering a comeback bid for governor in 2018.
Whether Mr. Trump permanently realigns the party around his style and platform may depend on how much he remains true to what could be called Trumpism.
Mr. Graham believes that the president is not as wedded to some of his nationalist policies as his supporters want to believe.
“The best thing that could happen to Trump and the future of the Republican Party is for Trump to fix a broken immigration system,” Mr. Graham said.
By calling last week to offer his support to a handful of Republican senators that Mr. Bannon had named as potential targets, the president demonstrated he would not blindly follow his former adviser.
Establishment Republicans are attempting to convince Mr. Trump that “if you join with Bannon, you cut your own throat,” Mr. Graham said, because it could lead to an impeachment effort by a Democratic-controlled Congress.
But these arguments cause the early Trump enthusiasts only to roll their eyes. The party establishment, these Trump backers say, wants to govern as if the election never happened.
“They still think the election was about Trump’s personality,” Ms. Ingraham said. “It wasn’t. It was his ideas.”