Early in the interview, McCain mentioned that he has been talking with President Obama about immigration reform. When I asked if he had also raised Syria, where McCain has sharply criticized administration passivity, he said no: “I don’t want to get into an argument with the president.” That’s interesting for a combative man who often can’t resist a zinger.

McCain said he is talking bipartisanship now because “I really believe the American people are fed up.” He joked about a survey showing that Congress is less popular with the public than a colonoscopy as evidence that “we are really in serious trouble,” and that “Americans want us to work together.” He pointed to compromises he’s trying to work out with Senate Democrats such as Carl Levin, Chuck Schumer and even Majority Leader Harry Reid.

The centerpiece of McCain’s new outreach is his engagement with Obama, which reverses a long period of frosty relations that culminated in his recent battle against the nomination of Chuck Hagel as defense secretary. When I asked if the Hagel attacks were too partisan, he repeated his disagreements on principle with the nominee but then conceded: “I plead guilty to being combative, to being zealous, to overreaching sometimes.”

During Obama’s first term, McCain said, he tried to reach out on issues such as immigration and was spurned. But here, too, he was self-critical: “I will admit to not cooperating as much as I should have.” He said he’s now eager to work with Obama on immigration reform, campaign finance, sequestration and a “grand bargain” on budget issues.