Bannon Put a Target on His Back. McConnell’s Answer: ‘Ha-Ha.’

President Trump’s former chief strategist wants him gone. His conference is fractious. But Mitch McConnell, the Senate majority leader, is pressing on to give Mr. Trump a legacy.

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.”

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To that, Mr. McConnell laughed. “You can write that down,” he said in an interview on Friday. “I laughed. Ha-ha. That’s a perfect response.”

Villainized by the president’s populist wing, Mr. McConnell nonetheless is pressing forward with a conservative agenda that he hopes will give Mr. Trump some big wins — and perhaps a legacy. He knows he must pass a tax overhaul in the coming weeks if his party is to have any hope of holding on to a united Congress next year — and if he is to remain majority leader. Meantime, he is trying to remake the nation’s judiciary, stocking the bench with Mr. Trump’s judicial nominees.

At 75, Mr. McConnell is a man of few words but many sayings. Among his favorites: “Losers go into another line of work and winners come to Washington to make policy.” And: “When you’re hit with a pebble, respond with a boulder.”

The target of that boulder would appear to be Mr. Bannon, a man whose name he refuses to utter, favoring “this particular individual” or “that particular element of our party,” or simply “they.”

“Their specialty is nominating people who lose in November,” Mr. McConnell said acidly, adding, “When they prevail, and they haven’t done that in recent years, we lose, and our intention in 2018 is they will not prevail anywhere.”

Mr. Bannon has been urging Senate candidates to pledge to vote against Mr. McConnell for majority leader, and he is making his campaign strikingly personal, “because the Senate and Mitch McConnell have been the most outrageous in their lack of support of President Trump’s agenda,” he said.

“Why Mitch McConnell?” Mr. Bannon asked. “Because the institution of the majority leader has so much power, and he has used that power to, quite frankly, thwart President Trump’s agenda.”

Mr. McConnell shot back: “Virtually everyone he has criticized, including myself, supports the president over 90 percent of the time.” He added: “The only way the president’s agenda doesn’t get enacted is if this particular element were to defeat enough senators in the general election to hand the Senate over to Democrats. That’s the only possible outcome if this kind of mentality were allowed to prevail. But I assure you it will not. It will not.”

The battle with Mr. Bannon puts the leader in a precarious position. On the one hand, he is trying to improve his tenuous relationship with Mr. Trump. On the other, he finds himself fending off attacks from one of the president’s closest allies.

“Mitch will be very calm, he’ll be very strategic, he’ll be very surgical and he will eventually eviscerate Mr. Bannon, and Bannon won’t even know what happened to him,” said Bill Stone, a former chairman of the Republican Party in Louisville who is close to Mr. McConnell. “Bannon is dealing with a man of intellect and a man of experience and a man of patience and resolve like he’s never met in his life.”

Senator Lamar Alexander, Republican of Tennessee and one of Mr. McConnell’s closest friends in the Senate, said the leader is paying scant attention.

“Mitch is experienced, he’s tough, he’s purposeful,” Mr. Alexander said. “He’s not deflected by irrelevant attacks.”

But the denizens of “McConnell World,” as the leader’s allies like to call themselves, are not so indifferent. They plan a campaign that will attack Mr. Bannon personally and seek to undermine his credibility by spotlighting his controversial comments and linking him with white nationalist groups.

The first hints of that strategy have surfaced in the press and on social media. Mr. McConnell’s former chief of staff, Josh Holmes, referred to Mr. Bannon as a “white supremacist” in a recent interview with The Hill newspaper. And the Senate Leadership Fund, a political action committee closely aligned with Mr. McConnell, recently took to Twitter to circulate a newspaper headline that called Mr. Bannon an anti-Semite.

For his part, Mr. Bannon called the charges “a hundred percent media fabrication” and the refuge of opponents that have nothing else. “They think the only way they can run is by smearing you to be a nativist, a misogynist, a racist, a homophobe,” he said. “Just go down the line.”

(A recent article in BuzzFeed News used leaked documents and emails to directly link Mr. Bannon and his publication, Breitbart News, to the right-wing provocateur Milo Yiannopoulos and some of the most extreme elements of the rising white supremacist movement.)

Billy Piper, a lobbyist and former chief of staff to Mr. McConnell, sees trouble in the brewing fight.

“The worst fights are often the inside-the-family fights,” Mr. Piper said. “If we don’t navigate these waters the right way, I think the inevitable result is losing seats, and that’s not in any Republicans’ interest and certainly not in the president’s interest. It’s challenging, and McConnell is at the center of that.”

Mr. McConnell has long been celebrated as a brilliant tactician, but he is struggling to govern with just a two-vote majority, and his record of legislative accomplishments this year is thin. He is still grappling with the fallout from the Senate’s failure to repeal the Affordable Care Act.

“There’s no way you can put lipstick on that pig and make it look good,” said Trent Lott, a former Senate Republican leader.

Mr. McConnell has also had a difficult relationship with Mr. Trump. They spent months feuding with one another, a conflict that reached a nadir in August, when Mr. McConnell privately told allies he feared Mr. Trump could not salvage his presidency.

“He has to use considerable diplomacy working with the White House and elements of the administration,” said Richard G. Lugar, a former Republican senator who lost a re-election primary to a Tea Party challenger in 2012, who then lost the Indiana seat to a Democrat. “He understands human nature and the differing ambitions of people. But also he understands his responsibility. He’s the leader. He has to produce.”

The two worked to patch things up during a White House lunch last month, followed by a 45-minute impromptu news conference in the Rose Garden that left the leader feeling buoyed — and fellow Republicans feeling relieved.

“They are both focused on the tax agenda, and I think the president realizes that he needs Mitch in order to accomplish his agenda,” said Senator Susan Collins, Republican of Maine.

And after a string of legislative losses, Mr. McConnell can at least point to one win: The Senate recently confirmed four circuit court judges, bringing to eight the number of federal appeals court judges the chamber has confirmed during Mr. Trump’s presidency. Afterward, Mr. Trump rewarded him with enthusiastic Twitter praise: “Our courts are rapidly changing for the better!”

Mr. McConnell makes the case that Mr. Trump’s most lasting legacy will come from remaking the federal judiciary by putting conservative jurists on the bench — including Justice Neil M. Gorsuch of the Supreme Court, who was seated after Mr. McConnell refused to allow hearings on Merrick Garland, former President Barack Obama’s nominee.

Mr. McConnell said that “transforming the judiciary” is his No. 1 priority, even higher than the tax overhaul. “The most important decision I’ve made in my political career,” he said, “was the decision not to do something; it was the decision not to fill the Supreme Court vacancy created by the death of Justice Scalia.”

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