“He is the devil they know and a very pragmatic leader,” said Senator Kevin Cramer, Republican of North Dakota, about Mr. McConnell and Senate Democrats. “And there is no one more shrewd.”
Mr. McConnell is a stalwart backer of maintaining financial assistance to Ukraine despite growing reservations in his own party, and he has the influence and record to keep a majority of his fellow Senate Republicans on board. He has also made it very clear that he wants to avoid a government shutdown and shares the view of Senate Democrats that federal spending has to be higher than what House Republicans are pursuing. And he has suggested that initiating an impeachment of Mr. Biden is not a great idea.
Democrats who often rip Mr. McConnell are refraining from doing so right now.
“There are extremes, mainly in the House, that I worry about, but I think he speaks for the mainstream Republican Party on most issues,” said Senator Richard J. Durbin of Illinois, the No. 2 Democrat, who had a lengthy conversation on the floor with Mr. McConnell about his health when the Senate convened Tuesday after a long summer recess. “He can play an important role in his own ranks in helping us come up with a bipartisan solution to our challenges.”
Mr. Biden, who has a track record of negotiating with Mr. McConnell, was among the first to reach out to the Republican leader last week after the episode in Kentucky and later offered public assurances about his condition. Officials in the Biden White House see Mr. McConnell as a figure they can depend on to avert a crisis, even though he might hold on to his cards until the last possible second.
It is a sensitive situation for both sides. Mr. McConnell is not particularly keen to be caught working hand in hand with Democrats, further infuriating his far-right critics, who already see him as a charter member of the swamp and what some of them call the “uniparty” mind-set in Washington. And Democrats do not want to be seen as cozying up to Mr. McConnell after their experiences dealing with him in a long string of toxic confrontations, such as when he blocked President Barack Obama from filling a Supreme Court seat for a year, keeping it open until it could be filled by Donald J. Trump.