About halfway into his Texas rally on Saturday evening, Donald J. Trump pivoted toward the teleprompter and away from a meandering set of grievances to rattle off a tightly prepared list of President Biden’s failings and his own achievements.

“Let’s simply compare the records,” Mr. Trump said, as supporters in “Trump 2024” shirts cheered behind him, framed perfectly in the television shot.

Mr. Trump, who later went on to talk about “that beautiful, beautiful house that happens to be white,” has left increasingly little doubt about his intentions, plotting an influential role in the 2022 midterm elections and another potential White House run. But a fresh round of skirmishes over his endorsements, fissures with the Republican base over vaccines — a word Mr. Trump conspicuously left unsaid at Saturday’s rally — and new polling all show how his longstanding vise grip on the Republican Party is facing growing strains.

In Texas, some grass-roots conservatives are vocally frustrated with Mr. Trump’s backing of Gov. Greg Abbott, even booing Mr. Abbott when he took the stage. In North Carolina, Mr. Trump’s behind-the-scenes efforts to shrink the Republican field to help his preferred Senate candidate failed last week. And in Tennessee, a recent Trump endorsement set off an unusually public backlash, even among his most loyal allies, both in Congress and in conservative media.

The Tennessee episode, in particular, showed how the Make America Great Again movement that Mr. Trump birthed is maturing to the point where it can, at times, exist separate and apart from — and even at odds with — Mr. Trump himself.

Mr. Trump remains, overwhelmingly, the most popular and powerful figure in the Republican Party. He is the polling front-runner in 2024, an unmatched fund-raising force and still able to fill fairgrounds with huge crowds. But after issuing roughly 100 endorsements in races nationwide, Mr. Trump will face a gantlet of proxy tests of his political strength in the coming months, just as public polls show his sway over the G.O.P. electorate is not what it once was.

“Things feel like they’ve been shifting,” said Patrick Ruffini, a Republican pollster who regularly surveys Mr. Trump’s standing in the party. “It’s a strong attachment. It’s one that very likely would win a Republican primary today. But is it the same ironclad, monolithic, Soviet-like attachment that we saw when Donald Trump was the incumbent president? No, it is not.”

In a recent Associated Press survey, 44 percent of Republicans said they did not want Mr. Trump to run for president again, while a potential G.O.P. rival in 2024, Gov. Ron DeSantis of Florida, has narrowed the gap in other way-too-early snapshots of a hypothetical primary — new signs of potential vulnerability for the former president.

In a reversal from Mr. Trump’s White House days, an NBC News poll in late January found that 56 percent of Republicans now define themselves more as supporters of the Republican Party, compared to 36 percent who said they are supporters of Mr. Trump first.

The Trump-first faction had accounted for 54 percent of Republican voters in October 2020. The erosion since then spanned every demographic: men and women, moderates and conservatives, people of every age.

Among the biggest swings was in a group widely seen as Mr. Trump’s most loyal constituency: white Republicans without college degrees, who went from 62 percent identifying first with Mr. Trump to 36 percent.

Frank Luntz, a prominent G.O.P. pollster, said Republican support for the former president is moving in complex ways — simultaneously both intensifying and diminishing.

“The Trump group is smaller today than it has been in five years, but it is even more intense, more passionate and more unforgiving of his critics,” Mr. Luntz said. “As people slowly drift away — which they are — those who are still with him are even stronger in their support.”

Mr. Trump faces further complications to a comeback, including an ongoing investigation in Georgia over his attempt to pressure state officials to overturn the election and an inquiry in New York into his business practices.

Betting against Mr. Trump’s hold on the G.O.P. has been a losing proposition, both for pundits and Republican rivals, for the better part of a decade, and he retains broad support in the party apparatus itself. As the Republican National Committee holds its winter meeting in the coming days in Salt Lake City, the party’s executive committee is expected to discuss behind closed doors whether to continue paying some of the former president’s personal legal bills.

Even some Trump-skeptical Republican strategists note that any softening of support has come after a year in which Mr. Trump did not seek to command public attention as thoroughly as he can.

He was back in the spotlight at Saturday’s Texas rally, an event that had the feel of a music festival, with anti-Biden chants of “Let’s go Brandon!” breaking out spontaneously. Amid the “Trump Won” flags, however, some conservative activists grumbled about the endorsement of Mr. Abbott, criticizing the governor’s early Covid-19 lockdowns and management of the border

On stage, Mr. Abbott himself faced shouts of “RINO” — for “Republican in name only” — and some boos, which he overwhelmed by leading the crowd in a chant of “Let’s go Trump!”

In his remarks, Mr. Trump seemed to be guarding his far-right flank when he declared that, “if I run and I win,” he would consider pardoning people who participated in the Jan. 6 attack on the Capitol last year.

One key split that has emerged between Mr. Trump and his base is over vaccines. He has been jeered at past appearances — both when urging supporters to get vaccinated and after he said he got a booster shot himself — and he now focuses on opposing federal mandates, while simultaneously trying to take credit for the speed of the vaccines’ arrival.

Mr. Trump notably avoided the word “vaccine” on Saturday, referring only to “Operation Warp Speed” — his administration’s effort to produce a vaccine.

Jennifer Winterbauer, who has “We the People” tattooed on her forearm, got to the Trump rally — her sixth — days in advance, sleeping in her truck to be among the first in line. She said she believed Mr. Trump was “sent by God to save this country.” Still, she disagrees with him on the vaccine.

“I don’t think he should be promoting it at all,” she said. “I’ve had Covid and I’ve had the flu, and the flu was much worse.”

Vaccine and Covid policies have also been the subject of simmering tensions with Mr. DeSantis, who has declined to say if he received a vaccine booster. Mr. Trump said “gutless” politicians dodge such questions.

Mr. Ruffini polled Mr. Trump vs. Mr. DeSantis last October and again this month. Then, Mr. Trump led by 40 percentage points; now, the margin is 25. But among Republicans familiar with both men, the gap was just 16 points, and narrower still, only nine points, among those who liked them both.

“His voters are looking at alternatives,” Mr. Ruffini said of Mr. Trump. While there is scant evidence of any desire for an anti-Trump Republican, Mr. Ruffini said, there is openness to what he called a “next-generation Trump candidate.”

At the Texas rally, David Merritt, a 56-year-old private contractor in a cowboy hat, described himself as “more of a Trump guy” than a Republican. But if he were not to run in 2024?

“Probably Ron DeSantis would be my next choice,” Mr. Merritt said. Because he was the most like Mr. Trump of the Republican candidates.

In Washington, Republican congressional leaders have diverged sharply in their approaches to Mr. Trump.

Representative Kevin McCarthy of California, the House minority leader, has been solicitous, huddling with Mr. Trump for roughly an hour last Tuesday at Mar-a-Lago to talk over House races and the political landscape, according to people familiar with the meeting. Mr. McCarthy is seen as keeping Mr. Trump close as he seeks to win the majority for his party this fall and the speakership for himself.

In the Senate, Mitch McConnell of Kentucky, the minority leader, is not on speaking terms with Mr. Trump, and his allies continue to court Gov. Larry Hogan of Maryland, an outspoken anti-Trump Republican, to run for Senate.

Beyond polling, Mr. Trump has repeatedly held up his “almost unblemished record” of primary endorsements as a barometer of his power. When Lou Dobbs, the pro-Trump media personality, asked Mr. Trump last week if the G.O.P. was still united behind him, he replied, “Well, I think so. Everybody I endorse just about wins.”

In North Carolina, Mr. Trump has promoted the Senate candidate he endorsed, Representative Ted Budd, by trying to convince Representative Mark Walker to abandon the primary and run for the House again. Mr. Walker threatens to divide the pro-Trump vote and help a third candidate, former Gov. Pat McCrory, a more traditional Republican.

On Thursday, Mr. Walker announced he was staying in the Senate race anyway.

Though Mr. Trump’s endorsements have sometimes been haphazard, despite ongoing efforts to formalize the process, few have drawn pushback more swiftly than his backing of Morgan Ortagus, who was an aide to former Secretary of State Mike Pompeo and was once floated as a possible White House press secretary.

Ms. Ortagus, with her family in tow, met with Mr. Trump at Mar-a-Lago last Monday and discussed a Tennessee House seat for which she is not even an official candidate yet, according to three people familiar with the meeting; by the next evening, Mr. Trump had endorsed her unannounced run.

“Trump has this completely wrong,” Candace Owens, a prominent figure in pro-Trump media, wrote on Twitter.

Ms. Owens threw her support to Robby Starbuck, a rival candidate with ties to the Trump activist movement. Representative Marjorie Taylor Greene of Georgia quickly endorsed Mr. Starbuck, too, and Representative Matt Gaetz of Florida, typically a staunch Trump ally, promoted one of Mr. Starbuck’s videos.

Gavin Wax, an outspoken pro-Trump activist and president of the New York Young Republican Club, who criticized the Ortagus and Abbott endorsements, said the political environment now made it possible to air such grievances. “It’s a lot easier to have these divisions begin to brew when he’s out of office,” Mr. Wax said of Mr. Trump.

“He still remains the top dog by a long shot, but who knows,” Mr. Wax said. “It’s one of those things where, a million cuts — it will eventually start to do damage.”

J. David Goodman contributed reporting from Conroe, Texas.