Ms. Pelosi, returning to the Capitol for the first time in the new year, met with members of her leadership team Tuesday evening. She told them that she still wanted more detail from Mr. McConnell about what precise procedures he would follow, in part to be able to pick her prosecutors, according to people with knowledge of her remarks.
A decision could come as soon as this week, though escalating tensions in the Middle East late Tuesday left the timing in doubt.
For his part, Senator Chuck Schumer of New York, the Democratic leader, promised to force a series of votes on John R. Bolton, the former White House national security adviser, and three other witnesses and document requests at the outset of the trial. Republicans could defeat the motions, but Democrats hope that some of them would instead break ranks, unwilling to go on the record against additional fact-finding in a trial of constitutional consequence.
“If you are afraid of the facts, if you are afraid of what would come out, if you want to cover it up, even in something as weighty and serious as impeachment, then you say no witnesses and documents,” Mr. Schumer said at a news conference.
He predicted a handful of Republicans could end up supporting summonses for witnesses like Mr. Bolton or Mick Mulvaney, the acting White House chief of staff, whom Mr. Trump effectively blocked from testifying in the House.
But for now, even moderate Republicans and those up for re-election this year were sticking with Mr. McConnell. Senators Susan Collins of Maine and Lisa Murkowski of Alaska have both expressed interest in potentially calling witnesses during the trial, but they have come around to Mr. McConnell’s argument that the matter should be debated only after opening arguments.
“I had certainly hoped that over the holidays, Leader McConnell and Senator Schumer would have been able to come to terms of an agreement,” Ms. Murkowski said on Tuesday. Instead, she conceded, they had become hopelessly “snarled up” in the debate over witnesses.