Speaker Mike Johnson on Wednesday found himself in a familiar position, teetering on the edge of failure as he worked to win over the regular holdouts in his party — and ultimately relying on President Trump himself to push legislation over the finish line to deliver his agenda.

In the past, this formula has worked for Mr. Johnson. He has used it to clear multiple steep hurdles despite his inexperience and the lack of trust he inspires in some rank-and-file Republicans who privately believe he is in over his head.

In Mr. Johnson’s deeply divided Republican Conference, the margins are always too slim, the bill is always teetering on the brink of death, there is always more trouble looming for the next step of the process and mini-rebellions are always flaring up.

Quashing them often involves sessions at the White House, where Mr. Trump plays the magnanimous host, sometimes offering photographs in the Oval Office or signing merch, to seal the deal. That was the case on Wednesday, as Mr. Johnson worked to put down multiple revolts in his party and bring the G.O.P.’s marquee legislation slashing taxes and social safety net programs to the floor for a final vote.

“This whole process has relied on a sense of inevitability that this will get done, no matter how steep the hill,” said Brendan Buck, a former top adviser to two Republican House speakers, John A. Boehner and Paul D. Ryan. “And this will get done, someway, somehow. And when it does, Mike Johnson will deserve all the credit in the world for keeping an even keel, and Donald Trump will deserve all the credit for being the muscle standing over the speaker’s shoulder.”

Mr. Trump has been the muscle, but also the flatterer. That method has yielded favorable results.

“It’s cool that the president knows my first name, I dig that,” Representative Tim Burchett, a hard-line Republican from Tennessee, said in March, just before he caved and voted for Mr. Trump’s budget plan that he had originally opposed. On Wednesday, Mr. Burchett, one of many ultraconservatives raising concerns about giving final approval to the domestic policy bill, seemed giddy in a video he posted on social media after leaving yet another meeting with Mr. Trump.