The only reason Mr. Enzi would “be in any difficulty is if there’s a weird group of Republicans who think compromise is akin to communism,” said Mr. Simpson, who called Mr. Enzi and Ms. Cheney “both wonderful people” and, like many here, does not want to have to choose.

Others in the Republican establishment are coalescing around Mr. Enzi, who indicated that he especially wants to continue serving now that he has won a long-sought seat on the Finance Committee.

In a local TV interview last month, Representative Cynthia M. Lummis, the state’s at-large Republican congresswoman, said pointedly that she would support Mr. Enzi if he ran again. And in a message many interpreted as a warning to Ms. Cheney, Ms. Lummis said she would run for the Senate if Mr. Enzi retired.

That message was echoed by Republicans at Mr. Enzi’s town hall sessions. The mere mention of Ms. Cheney to a woman after an event in Newcastle brought forth disapproving references to an article published a few days earlier in a Casper newspaper about a political organization based in California promoting her candidacy for Senate. (Ms. Cheney said through an aide that she had no connection to the group.)