WASHINGTON — Senator Mitch McConnell, the taciturn Republican leader, watched stoically from across the Capitol two years ago as Speaker John A. Boehner resigned rather than contend with mounting troubles, restive conservatives and a band of renegade Republicans looking to oust him.

Now it is Mr. McConnell who has a target on his back.

His party is smarting from losses at the ballot box last week in Virginia, New Jersey and off-year races across the country. A trio of Senate Republicans who are not running for re-election have gone rogue and feel no compunction to fall in line behind him. The Republican nominee for Senate, Roy S. Moore, has just been accused of improper sexual and romantic conduct with teenagers.

And Stephen K. Bannon, President Trump’s former chief strategist, is vowing to depose him, telling The New York Times that “I have an objective that Mitch McConnell will not be majority leader, and I believe will be done before this time next year.” Mr. McConnell, he added, “has to go.”