Instead, the response was crickets.

Ms. Collins and Senator Bill Cassidy, Republican of Louisiana, calmly pointed out that Mr. Trump had supported a much larger infrastructure plan in the past but failed to deliver. Mr. Portman, who had personally called Mr. Trump to encourage him to back the legislation, politely suggested that Mr. Trump change tactics and embrace the plan.

When the time came to vote to advance the measure on the Senate floor, the coalition of mostly moderate members found that, contrary to Mr. Trump’s efforts, the number of conservative senators supporting their plan had increased, not decreased — with members of Republican leadership, including Mr. McConnell and Senator Roy Blunt of Missouri, who is also retiring, joining their ranks.

Senator Kevin Cramer, Republican of North Dakota, said some of his constituents were “mad as hell” about his support for the bill — particularly about the idea of doing something that would make President Biden look good. But rather than follow Mr. Trump’s lead, he has made a point of talking up the agreement on conservative talk radio shows.

“I firmly believe that people — the longer they live with it, the more they look at it, the more they hear about it, the more they’ll like it, including conservatives,” Mr. Cramer said.

Several Republican aides said the developments left them feeling that while Mr. Trump’s influence over the Senate was not gone, he was diminished.

Indeed, many Republicans said they were puzzled over the point Mr. Trump was trying to make. The former president had proposed a $1.5 trillion infrastructure package while in office, so his opposition to a leaner bill seemed motivated either by personal pique or a simple desire to see his predecessor and the opposing party fail.

“It’s not really so clear what Trump’s substantive objection is here,” said Philip Wallach, a senior fellow at the conservative American Enterprise Institute. He’s certainly not saying doing an infrastructure bill is bad; he spent his whole four years talking about how great it would be. So all he’s really saying is, ‘Working with Democrats is bad.’ And for a lot of these senators from closely contested states, they figure their electoral base just doesn’t agree that bipartisanship is bad.”