“The Senate Democratic leader recently said that as long as he can try to use the trial process to hurt some Republicans’ re-election chances, quote, ‘it’s a win-win,’” Mr. McConnell said this week. “That’s what this is all about.”

Democrats bristle at the idea that they are playing politics and say that Mr. Trump put national security at risk by withholding military aid from Ukraine as leverage to force an investigation of a political rival and then stonewalled the House investigation of his actions.

In a tale of two chambers, the contrast between the House and Senate was on full display Wednesday. House Democrats showcased their selection of impeachment prosecutors and the ritualistic delivery of the articles of impeachment across the Rotunda while Senate Republicans treated the matter like a hot potato, appearing in no hurry to take possession of the charges. Mr. McConnell promptly put off until Thursday the formal reception of the paperwork.

“The far left has been desperate to get rid of President Trump since Day 1, and that has been made abundantly clear throughout this process,” said Senator Todd Young, Republican of Indiana, who nevertheless said he would try to weigh the merits of the case. “Now that the articles are being delivered and a trial will be held in the Senate, I will uphold my duty as an impeachment juror and carefully evaluate the legal arguments.”

Before the Clinton impeachment trial got underway, the full Senate gathered in the old chamber down a marble hallway from the Senate floor to work out their differences in a free-flowing private discussion that participants remember as a singular event during their service. They said the weight of what they confronted, and the historic surroundings of the chamber where illustrious senators of the past had roamed the floor, encouraged them to find common ground.

Mr. McConnell, in contrast, apparently wants nothing to do with the old Senate chamber. Republicans say he would prefer to stay out of the storied space for fear an all-hands meeting there would lend undue import to the trial and create an atmosphere in which some Republicans could decide to ally themselves with Democrats on procedural issues, effectively costing him control of the process.