They are also displeased that Mr. McConnell is trying to speed up the trial by capping the number of days the managers and defense lawyers have to present their cases, and that his proposal would not automatically include the House’s impeachment evidence as a part of the Senate trial record.

This will not look like a typical Senate colloquy.

Given the unusual requirements of a Senate impeachment trial, the resolution will be debated in the open not by the senators themselves, but by the House managers and the defense team, acting as proxies for the Democrats and Republicans.

If senators want to engage in their own debate, they will have to go into private session, closing the Senate doors, kicking out reporters and shutting off the television cameras until they reach a resolution.

Democrats are ready to force amendment votes that would call witnesses or evidence to pressure moderate Republicans like Susan Collins of Maine, Lisa Murkowski of Alaska, Cory Gardner of Colorado and others, but Mr. McConnell is expected to hold all 53 Republicans to his position. Each such vote could take up to two hours.

Both sides expect debate to go late into the night.

Oral arguments could begin as early as Wednesday.

If the Senate adopts Mr. McConnell’s proposal on Tuesday, the trial could move promptly to opening arguments on Wednesday.

As the prosecution, the House managers will present their case first. They will lay out in detail their case that Mr. Trump pressured Ukraine to announce investigations into his political rivals by withholding almost $400 million in military aid and a White House meeting for its leader — and then concealed it from Congress by blocking witnesses and documents.

Next up will be the president’s defense team — including Ken Starr, the former independent counsel who pursued Mr. Clinton, and Alan Dershowitz, a famed constitutional law scholar — who intend to argue that Mr. Trump was merely acting in the United States’ best interest and that the charges constitute little more than political attack by Democrats.