(Image source: CBS / Gawker ) BY ELIZABETH HAGEDORN President Obama and outgoing Secretary of State Hillary Clinton sat down for a rare joint interview on CBS’s “60 Minutes” -- further fueling speculation over what’s next for Clinton. The President piled on the praise for his top diplomat, in an interview that carries with it a considerable amount of significance, as it’s the first time Obama has given an interview alongside anyone other than the First Lady. With more on that, here’s MSNBC’s Chris Matthews. “It’s like their politically married. This is a fascinating event. President of the United States, with a duet with the Secretary of State of the United States. This is big time, something’s up here. Something’s up.” The two have certainly come a long way since the days of “You’re likeable enough, Hillary.”  And they acknowledged to CBS’s Steve Kroft just how unlikely the prospect of the interview would have seemed to them five years ago. "A few years ago it would have been seen as improbable because we had that very long, hard primary campaign." The former foes appear to have reached some level of friendship. Reflecting on their relationship, a writer for the National Journal says, “[There] is a certain personal chemistry that was easily overlooked four years ago. Both the president and Clinton are extremely self-confident individuals... who despise Washington’s political culture. These are no-drama types who believe posturing and preening are beneath them...” Kroft probed Clinton over the terrorist attacks in Benghazi, her health, and the administration’s reluctance to  military intervene in Syria. But the question on everyone’s minds -- will she run in 2016? -- well, both the President and Secretary of State managed to dance around it. “You guys in the press are incorrigible … I was literally inaugurated 4 days ago.” “As you know Steve, I’m still Secretary of State. So I’m out of politics, and I’m forbidden from even hearing these questions...” One person likely tuning in to Sunday’s interview was Vice President Joe Biden, who appears to eyeing a White House run, as well. It’s widely believed, however, that Clinton would be the Democratic frontrunner in 2016 should she choose to run. The interview, while just short of an official endorsement from the President, had BuzzFeed’s Zeke Miller tweeting , “If Hillary runs in 2016, she should just buy 30 minutes of airtime in the Democratic primary and air this interview straight.” Looking to the future, the Washington Post’s Chris Cillizza writes, “Regardless of what’s next for Barack and Hillary, what has happened over the past six-ish years between the two of them is a remarkable political tale. They are now, by all accounts, friends.” The latest Washington Post/ABC News poll shows Clinton’s approval ratings at 67 percent -- a record high for her. She’s expected to leave her post as Secretary of State on Friday.