“I’m going to try to stay in a position where I can have input to the president,” Mr. Graham, 62, said in a lengthy interview. “I can help him where I can, and he will call me up and pick my brain. Now, if you’re a United States senator, that’s a good place to find yourself.”
“He’s very popular in my state,” Mr. Graham continued. “When I help him, it helps me back home. And I think it probably helps him to be able to do business with an old rival who’s seen as a deal maker.”
To Republican critics of Mr. Trump, Mr. Graham is risking his reputation with such a calculus.
“Lindsey Graham knows better,” said Peter Wehner, who advised former President George W. Bush and is a contributing opinion writer for The New York Times. “Deep in his heart, he must know that Donald Trump is fundamentally unfit to be president, and he has to pretend that Trump is. And when you engage in a game like that, there’s often a cost to it.”
Mr. Graham is willing to take the risk. Twice in the last two weeks, he has been the president’s golf partner. (Mr. Trump is better, he says.) There have been one-on-one huddles in the Oval Office. And two days before the series of phone calls last week, Mr. Trump brought Mr. Graham along for a 15-minute helicopter flight from Joint Base Andrews in Maryland to the White House after a trip aboard Air Force One.
Few people ever get to join the president on Marine One. Likely no one has been invited to fly as a guest aboard the presidential helicopter after calling the commander in chief “the world’s biggest jackass,” as Mr. Graham once said of Mr. Trump. (Mr. Trump, then a candidate for the White House, responded by calling Mr. Graham “an idiot.”)
Somehow, though, a president who is famous for nursing grudges appears to have put the past behind him. And despite their differences — on immigration, race relations and isolationism — Mr. Trump and Mr. Graham have become Washington’s oddest odd couple, working together to repeal the Affordable Care Act, cut taxes and increase military spending.
“We have become friends while working to get health care and tax cuts for the American people,” Mr. Trump said in an email response to a question about their relationship. “Senator Graham is a fighter and a good person.”
Credit Doug Mills/The New York Times
That hasn’t always been Mr. Trump’s opinion of Mr. Graham. This summer, after the senator criticized the president’s comments about the racial violence in Virginia after the death of a protester, Heather Heyer, Mr. Trump lashed out.
“Publicity seeking Lindsey Graham falsely stated that I said there is moral equivalency between the KKK, neo-Nazis & white supremacists, and people like Ms. Heyer,” the president said on Twitter. “Such a disgusting lie. He just can’t forget his election trouncing. The people of South Carolina will remember!”
Some Republicans said they were not entirely surprised by Mr. Graham’s embrace of the president.
“He’s being very pragmatic,” said Mike Murphy, a longtime Republican consultant who is also an outspoken critic of Mr. Trump’s, adding that the senator was engaged in “a delicate dance.”
“I don’t give him any demerits on supporting him where they agree on policy,” Mr. Murphy said.
Health care has been one of those areas. Mr. Graham first opposed, then supported, the Senate’s unsuccessful effort to pass a narrow “skinny” repeal of the Affordable Care Act this summer. Frustrated and unwilling to give up, Mr. Graham used a private meeting in the Oval Office to urge support for a plan that relies on block grants to states.
When that plan stalled, the private meeting gave it new life, according to former Senator Rick Santorum, Republican of Pennsylvania, who has been helping develop the block grant proposal.
“We were getting nowhere until Lindsey met with Trump, and Trump said, ‘Hey, you’ve got to start working with these guys,’” Mr. Santorum recalled. “They were paying us lip service until Trump said, ‘Hey, I want this to happen.’ ‘As Lindsey got Trump more engaged, the White House got more engaged.”
Mr. Graham said he was trying to help Mr. Trump turn his “message into legislative success,” adding: “I think what he sees in me is a guy that is willing to try to find a way to make something happen. I’m willing to do things that sometimes other Republicans won’t.”
But Mr. Wehner cautioned that Mr. Graham must be careful.
“There’s a rule of thumb when it comes to Donald Trump: Everybody who gets close to him or supportive of him in one way or another is stained by him,” he said. “I suspect that Lindsey Graham is going to find that out the hard way. He’ll be used.”
The senator insists he is frank with Mr. Trump when he disagrees with him. For instance, Mr. Trump wants to do away with the filibuster, the Senate rule that requires a 60-vote threshold to pass most legislation. Mr. Graham wants to keep it. “We argue about this all the time,” the senator said.
Looking ahead, Mr. Graham envisioned working with the president on issues as varied as an immigration overhaul — Mr. Trump has “credibility no one else has” — and a minimum-wage increase, which Mr. Graham says he intends to introduce when the Senate considers revamping the tax code. He said Mr. Trump “loved” the idea.
Mr. Graham’s Republican colleagues in the Senate, meanwhile, are keeping close watch on the newfound friendship.
“Lindsey and the president are the most interesting couple in Washington,” said Senator Bill Cassidy, the Louisiana Republican who is Mr. Graham’s co-sponsor on the health care measure. “They kind of fuss with each other, and then they go play golf.”
Mr. Corker offered another possible reason for their bonding: “Lindsey’s fun!”
Mr. Graham says much the same about the president: “He’s a lot of fun. He’s just like me. He’s just a B.S. artist on the golf course.”