The arguments are scheduled to arrive while Washington prepares for Tuesday’s opening of the second impeachment trial of Mr. Trump in just over a year, a dubious record that promises to leave a mark on both parties. For Democrats now in control of Congress and the White House, the proceeding threatens to complicate Mr. Biden’s attempts to quickly pass a nearly $2 trillion coronavirus stimulus bill. Republican leaders worry that days of intense focus on the former president’s mendacious campaign to overturn his election loss could further cleave their party.

The precise rules and duration of the trial remained unsettled as senators continued to haggle over whether to allow live witness testimony and how much time to grant the prosecution and defense. Still, there appeared to be an overwhelming bipartisan interest in quickly reaching a verdict, possibly as soon as this weekend.

On Monday, Senator Chuck Schumer, Democrat of New York and the majority leader, is expected to share a draft of the rules negotiated with Senator Mitch McConnell of Kentucky, his Republican counterpart. Senators will vote to adopt them once the trial begins on Tuesday.