In the week since Mr. Trump skipped President Biden’s inauguration and decamped to his private club in Florida, it had become increasingly clear that his departure from the Oval Office had done little, if anything, to loosen his grip on rank-and-file Republicans in Congress.

While few have defended his conduct, many fewer have dared to back the impeachment push. The 10 House Republicans who did join Democrats in voting to impeach him faced fierce backlash, and in the Senate, constituents were flooding offices with phone calls indicating they expected their senators to stand behind Mr. Trump.

“Let’s face it: Many of the people there — they want to be re-elected, most of them,” said Bob Corker, a former Republican senator from Tennessee who retired in 2018 after clashing with Mr. Trump. “For those people, whose service in the Senate is their entire life, I’m sure just what they are hearing back home has an effect on them.”