The talks are complicated, with a lot of variables: how long the trial will last; how much time each side will get to present its case; whether any witnesses will be called, and if so, how many; how documentary evidence will be handled; and so on. There are questions about who will get to speak and where people will sit.

But the central question appears to be whether witnesses will testify. Mr. Trump has said he wants to call Hunter Biden, as well as Speaker Nancy Pelosi and Representative Adam B. Schiff, the chairman of the House Intelligence Committee, who led the fact-finding phase of the impeachment inquiry.

The McConnell camp worries that could open a “Pandora’s box,” as one person close to the senator said, clearing the way for other witnesses and lines of questioning that could reflect poorly on the president. But some House Republicans say it is important to do so.

“I understand their desire to just get it behind us, but the country needs to hear what a farce this was,” Representative Louie Gohmert, Republican of Texas and a member of the House Judiciary Committee, said Friday. “They really need to bring in witnesses. They are the chance to clean this mess up.”

The Senate has specific rules, revised in 1986, governing impeachment trials. Among other things, once the House adopts articles of impeachment and presents them to the Senate, the Senate must take them up at 1 p.m. the next day (unless it is a Sunday) and consider them six days a week (except Sundays) until it renders a judgment.

The chief justice of the United States presides over the trial, but the format is left to the Senate itself, which can proceed in several ways: The Republican and Democratic leaders may strike an agreement on one or more resolutions governing the proceedings, or, failing that, the resolutions may be adopted by a simple majority of 51 senators. Or there can be no resolutions at all, and senators can introduce motions as they go.