The tactic looms as a delicate proposition for Mr. McConnell and his Republican colleagues. First, they must mollify a mercurial president and Republican voters who will no doubt be incensed at the very idea of a Senate trial giving credence to the accusations that Mr. Trump improperly sought foreign help against a political rival. At the same time, they would need to demonstrate to the public that the Senate was taking its constitutional responsibilities seriously and not dismissing the House action out of hand.

In either regard, it would represent another tough vote for vulnerable Senate Republicans up for re-election in 2020, who would again have to choose between potentially alienating independents by siding with the president or angering the pro-Trump faction that dominates their party. It could also represent a risky vote for Democrats seeking re-election in swing states such as Michigan.

Democrats say they would keep the pressure on Republicans to make sure that the process for considering articles of impeachment against the president is equitable to both sides.

“If the impeachment process reaches the upper chamber, each and every Senate Republican will have the awesome responsibility of putting country over party and ensuring Leader McConnell allows a fair trial,” Senator Chuck Schumer of New York, the Democratic leader, said in a statement on Tuesday.

Mr. McConnell had other reasons to get out in front of questions about how he would handle impeachment. He needed to fend off what are certain to be demands from the president’s supporters to shut down the process or refuse to entertain the articles of impeachment even if it takes turning off the Senate lights and locking the doors. And to hold off those who demand another “nuclear option” to overturn the existing impeachment rules, Mr. McConnell also noted that it would require 67 votes to do so, not the simple majority vote both parties have used in recent years to reset Senate procedures.

That may have been a pre-emptive answer to Mr. Trump himself, who in times of frustration in the past, has sometimes criticized Mr. McConnell for being unwilling to use the “nuclear option” to circumvent rules that require 60 votes to advance most legislation.