The following script is from "The President and the Secretary of State" which aired on Jan. 27, 2013. Steve Kroft is the correspondent. Michael Radutzky, Maria Gavrilovic and L. Franklin Devine, producers.
There are few people we think we know more about than President Barack Obama and outgoing Secretary of State Hillary Clinton and everyone has an opinion about their politics, their marriages and a rivalry that is one of the richest in American history.
On Friday, we had the opportunity to sit down with the two of them side by side. The White House offered us 30 minutes, barely enough time to scratch the surface of their complicated personal and professional relationship, let alone discuss their policies on Iran and Israel, Russia and China, Egypt and Libya. There has been much speculation about their evolution from bitter opponents to partners in the corridors of power and the motivation for doing this interview. Now, you can be the judge.
Steve Kroft: This is very improbable. This is not an interview I ever expected to be doing. But I understand, Mr. President, this was your idea. Why did you want to do this together, a joint interview?
President Obama: Well, the main thing is I just wanted to have a chance to publicly say thank you, because I think Hillary will go down as one of the finest secretary of states we've had. It has been a great collaboration over the last four years. I'm going to miss her. Wish she was sticking around. But she has logged in so many miles, I can't begrudge her wanting to take it easy for a little bit. But I want the country to appreciate just what an extraordinary role she's played during the course of my administration and a lot of the successes we've had internationally have been because of her hard work.
Steve Kroft: There's no political tea leaves to be read here?
Secretary Clinton: We don't have any tea. We've got some water here is the best I can tell. But you know, this has been just the most extraordinary honor. And, yes, I mean, a few years ago it would have been seen as improbable because we had that very long, hard primary campaign. But, you know, I've gone around the world on behalf of the president and our country. And one of the things that I say to people, because I think it helps them understand, I say, "Look, in politics and in democracy, sometimes you win elections, sometimes you lose elections. And I worked very hard, but I lost. And then President Obama asked me to be secretary of state and I said yes." And so this has been just an extraordinary opportunity to work with him as a partner and friend, to do our very best on behalf of this country we both love. And it's something I'm going to miss a great deal.
Steve Kroft: It's no secret that your aides cautioned you against-- actually were against you offering Secretary Clinton this job. And you were just as determined not to take it. And you avoided taking her phone calls for awhile because you were afraid she was going to say no. Why were you so insistent about wanting her to be secretary of state?
President Obama: Well, I was a big admirer of Hillary's before our primary battles and the general election. You know, her discipline, her stamina, her thoughtfulness, her ability to project, I think, and make clear issues that are important to the American people, I thought made her an extraordinary talent. She also was already a world figure. And I thought that somebody stepping into that position of secretary of state at a time when, keep in mind, we were still in Iraq. Afghanistan was still an enormous challenge. There was great uncertainty in terms of how we would reset our relations around the world, to have somebody who could serve as that effective ambassador in her own right without having to earn her stripes, so to speak, on the international stage, I thought would be hugely important.
Steve Kroft: You've been quoted as thinking or telling people that there was no way you were going to take this job and you weren't going to let anybody talk you into it.
Secretary Clinton: Well, I would--
Steve Kroft: What did he say that night that made you--
Secretary Clinton: Well, I was so surprised, because, you know, after I ended my campaign, I immediately did everything I could to help the president get elected, because despite our hard-fought primary, we had such agreement on what needed to be done for our country.
President Obama: Made for tough debates, by the way, 'cause we--