“He leads, and if the conference expresses its will as different, then he leads that way,” said Senator Kevin Cramer, Republican of North Dakota.

Mr. McConnell has shown in the past that he can be pushed from his position if internal pressure becomes great enough. Fearing an embarrassing division among Republicans on a criminal justice overhaul, Mr. McConnell for years resisted putting the bipartisan legislation on the floor despite overwhelming support. Prodded by the president, Mr. McConnell finally relented in 2018 and the measure passed with almost 90 votes — including his own.

In the days leading to the disclosure of Mr. McConnell’s trial proposal, the focus was on whether it would guarantee witnesses, as sought by Democrats, or simply allow a future vote on the matter, following a bipartisan set of rules set in 1999 for President Bill Clinton’s impeachment trial.

But when the details became public on Monday night, only hours before a debate on them on the Senate floor, the proposal also included an unexpected compressed timetable for opening arguments — 24 hours over two days — and required a separate vote on accepting the House impeachment record into evidence, rather than taking it automatically, as had been done in the past.

Officials with knowledge about the developments said the White House sought the compressed time period. The president’s allies feared that allowing Democrats three days to present their case would allow them to drag it out through Saturday, ending the first week — and heading into the Sunday talk shows — with no formal response from the president’s defenders. The White House did not like that idea, and was not particularly concerned about the optics for Senate Republicans of squeezing the proceedings into marathon, 12-hour sessions that would stretch long into the evening.

But Republican senators quickly raised concerns privately, suggesting that the restrictions would open the door to harsh criticism that they were trying to short-circuit the trial — a claim they were eager to avoid — and also strayed too far from the precedents of the Clinton trial they were relying on to justify their stance on witnesses.