“The obvious challenge for everybody here is that they are working with a president with no tolerance for anyone to criticize” him, said Brendan Buck, a former counselor to the last two Republican House speakers, Paul D. Ryan and John A. Boehner.

Rather than acknowledging that Mr. Trump’s call with the Ukrainian president, in which he asked that the leader investigate a leading political rival, was inappropriate and moving on to a debate about whether that rose to impeachment, Mr. Buck continued, “they’re getting stuck wrapped around the axle of whether what the president did was wrong, or whether he even did it in the first place.”

In an attempt to rally and unify the conference, Mr. Trump joined a call with House Republicans on Friday afternoon, according to a person present who spoke on the condition of anonymity to discuss it. The president emphasized to lawmakers that Democrats were refusing to focus on solutions that would help the American people and instead trying to overturn the result of the 2016 election, the person said.