Yet during one of Obama’s toughest times as president, there was McCain, sitting down last week with him in the Oval Office for a private strategy session. At the urging of new White House chief of staff Denis McDonough, who has sought better ties with Republicans, Obama has had more substantive discussions with McCain in the past five months than he did in his first four years in office, according to associates of both men. Suddenly, the two are working together on issues ranging from immigration to the deficit.

“I’m getting nervous,” said Sen. Lindsey Graham (R-S.C.), McCain’s closest friend in the Senate. “I told Denis McDonough, ‘I don’t know what you’ve done: You’ve hijacked him.’”

There are many reasons for the sudden détente, including the fact that both men share common ground on several big issues that could wind up defining their legacies. But it’s unclear whether the Obama-McCain alliance can disrupt the gridlock in Washington given both men are viewed skeptically by many conservatives…

“Ever since the election, we’ve had conversations and phone calls,” McCain told POLITICO in an interview. “And I think we share many agenda items that we can work on together, ranging from immigration reform, the prison in Guantánamo, to working perhaps on a grand bargain, security of our embassies and consulates. There are a bunch of issues that we share.”