The president had been excited about the event for days, focused more on it, and tried to overturn the electoral college vote than anything else. On the way to Wednesday, some advisors said privately that Mr. Trump appeared to believe that Mr. Pence could legally pass the election to him in his role as chairman of the vote.

At one point, Mr Trump told the Vice President that he had spoken to Mark Martin, the former chief justice of the North Carolina Supreme Court, who had told him that Mr Pence had that authority. Mr. Pence had assured Mr. Trump that he did not. Mr Trump had the Vice President defend his case in a meeting with attorneys whom Rudolph W. Giuliani helped draft.

Both parties admitted they had no clear picture of how many Republican senators could ultimately vote in favor of Mr Trump’s conviction.

Mr Toomey said Mr Trump has been “kind of mad” since the election and has effectively “disqualified” from ever running for office again. But a day after calling Mr. Trump’s behavior “incontestable,” Mr. Toomey argued that impeachment would be impractical as Mr. Trump was already on his way to the exit.

“I think the best way for our country, Chuck, is for the president to step down and leave as soon as possible,” he told host Chuck Todd on NBC’s Meet the Press. “I admit that may not be likely, but I think that would be best.”

Speaking to staff about the prospect of yet another impeachment trial, Mr. Trump was struck by the fact that few people on his defense team would be part of a new trial in last year’s Senate trial.

Jay Sekulow, who has served as his lead personal attorney, and two other private attorneys, Marty Raskin and Jane Raskin, will not attend any future impeachment defense, according to a person briefed on the planning, as will Pat A. Cipollone, attorney for the White House or Patrick F. Philbin, his deputy.