That could put him at odds with Senate Republicans whose interests are not the same as his. Absent dramatic new revelations, Mr. Trump appears assured of escaping conviction in the Senate since that would require a two-thirds vote. But he has been eager to call witnesses Senate Republican leaders are not anxious to summon, like former Vice President Joseph R. Biden Jr. and the unidentified C.I.A. whistle-blower whose complaint kicked off the impeachment inquiry.

Senator Mitch McConnell of Kentucky, the Republican leader, talked with Mr. Trump this week about holding a relatively abbreviated trial without calling witnesses, according to a person briefed on the conversation. Mr. McConnell envisioned a trial lasting about 10 to 12 days and sought to convince Mr. Trump that a quick acquittal without the spectacle of a parade of witnesses would be better for the president.

Mr. Trump seemed amenable, but he often changes his mind and no one is certain where he will end up. He sent his White House counsel, Pat A. Cipollone, and his legislative affairs director, Eric Ueland, to meet with Mr. McConnell at the Capitol on Thursday.

Still to be determined is who will represent Mr. Trump at the trial, whether it is short or long. Mr. Trump is said to have talked with several prominent lawyers about taking on his case, but multiple people said that Mr. Cipollone had resisted bringing in new representation, leaving him to serve as lead counsel.

Among those being considered is Alan Dershowitz, the famed lawyer who represented O.J. Simpson, Jeffrey Epstein, Roman Polanski and Mike Tyson and has defended the president on television. But he would probably offer guidance from the private legal team outside the White House as Mr. Cipollone takes the lead.

For Mr. Trump, the impeachment battle has become the defining test of his presidency, weighing him down and charging him up all at once.

Some advisers said the collective burden of three years in office and the nonstop investigations had taken a toll on him. People who have spent time around him lately said he seemed fatigued and might have gained weight. Some who work in the White House have noticed that he seems more standoffish, less likely to engage in small talk with those outside his inner circle.