With Mr. Trump so willing to criticize, his aides have been emboldened to fan the discontent. That was jarringly illustrated this week when Politico revealed that Mr. Ayers told another group of party donors that they should “purge” disloyal Republicans.

“If I were you, I would not only stop donating, I would form a coalition of all the other major donors, and just say two things,” he said. “We’re definitely not giving to you, No. 1. And No. 2, if you don’t have this done by Dec. 31, we’re going out, we’re recruiting opponents, we’re maxing out to their campaigns, and we’re funding ‘super PACs’ to defeat all of you.”

To the consternation of Republican lawmakers, Mr. Pence let Mr. Ayers’s comments stand.

“That was amateur hour,” said Mr. Corker, adding that it also happened to be “the general modus operandi” of the administration.

To maintain their grip on the party, Republican leaders and their supporters are scrambling to recruit new allies and pleading with their loyalists to remain in Washington — not always with success.

A battery of Republican senators had telephoned Tennessee’s governor, Mr. Haslam, a popular and wealthy establishment figure, and invoked Mr. Moore’s primary election victory to argue that the identity of the party was on the line, according to a Republican official familiar with the line of argument. Mr. Corker and Senator Lamar Alexander of Tennessee led the charge.

On Thursday, he turned them down.

In a sign of their determination to retain the seat, establishment-aligned Tennessee Republicans immediately began trumpeting R. Brad Martin, a former state legislator and onetime chief executive of Saks as a potential candidate. Representative Marsha Blackburn, a conservative, could prove the most formidable candidate, though.