Ms. Pelosi, in her own remarks on Tuesday, conceded that Democrats were unlikely to see a change of heart from Republicans anytime soon. Still, she argued that a pattern of obstruction of justice by the president was becoming clearer by the day.

“Trump is goading us to impeach him,” she said at a Cornell University event in Manhattan. “That’s what he is doing; every single day he is just, like, taunting, taunting, taunting. Because he knows that it would be very divisive in the country. But he doesn’t really care; he just wants to solidify his base.”

Ms. Pelosi said she was pushing her caucus not to take the bait, but instead to try to line up the facts and build a public case. But nearly three weeks after the release of a redacted version of Mr. Mueller’s 448-page report, that is proving more difficult than Democrats anticipated.

As the Judiciary Committee received word from Mr. McGahn and the White House that he would not comply with its subpoena, committee staff members were preparing for a Wednesday morning vote on contempt for Mr. Barr.

Justice Department officials and lawyers for the committee met once again on Tuesday to try to hash out a compromise to dial back the escalating tensions. They traded counteroffers, but ultimately the discussions ended acrimoniously.

The Justice Department was also in a standoff with the House Intelligence Committee over a bipartisan request by its chairman and top Republican for access to all intelligence and counterintelligence information collected in the course of Mr. Mueller’s work. A committee aide indicated on Tuesday that discussions with department officials did not appear to be progressing and that the Democrat-led panel would soon turn to a subpoena.

The case of Mr. McGahn, who is cited more than any other witness in the Mueller report, was narrower, but the White House actions threatened to wall off a central witness.