McCain is gambling his bid for the White House on success in the war. When Pelley sat down with him in Iraq, he said Americans can't lose their nerve now, just when he thinks there's reason to hope.
"I believe that we can succeed and I believe the consequences of failure are catastrophic. Those who say 'Just withdraw,' then you say, 'What next?'" Sen. McCain says.
"I wonder at what point do you stop doing what you think is right and you start doing what the majority of the American people want?" Pelley asks.
"Well, again, I disagree with what the majority of the American people want. Failure will lead to chaos, withdrawal will lead to chaos," McCain replies.
With pressure to withdraw building at home, McCain landed in the midst of the Baghdad surge and did something that would have been unthinkable a few weeks ago.
The new commander, Army General David Petraeus, sealed McCain inside the latest armored Humvee, soldiers call it a "Full Up Frag 5," and took McCain on a Sunday drive to the market.
Gen. Petraeus wrote the book on the Bush administration's new strategy. He started eight weeks ago, moving U.S. troops off bases and into neighborhoods to clear and hold the streets. The centerpiece is the al Shorja market. Two months ago it was devastated by a car bomb. Now the Army has banned vehicles and laid on extra security.
Petraeus brought McCain to a rug shop, an ordinary scene, until you step back to see the 22 soldiers outside. Inside, McCain did his own reporting, asking the rug merchant, "In the last two months are things better or worse?"
The merchant said things are better, but, he said, there are snipers in the neighborhood that sometimes paralyze the market. The tour of the bazaar seemed, well, a little bizarre. The delegation played the role of tourists while surrounded by enormous firepower. The guns, though, couldn't protect McCain from his own words.
The week before, trying to build support for the surge, he said this on television: "General Petraeus goes out there almost every day in an unarmed Humvee."
And he said this on the radio: "There are neighborhoods in Baghdad where you and I could walk through those neighborhoods today."
Those words came back to haunt him in a Baghdad news conference. And he made it worse.
"Senator McCain, I just read in the Internet that you said there are areas in Baghdad that you can walk around freely," a reporter asked.
"Yeah, I just came from one," McCain replied.
But backing up that stroll through the market were ten armored Humvees, soldiers with rifles, and two Apache attack helicopters circling overhead.
"I understand why they would provide me with that security but I can tell you if it had been two months ago and I'd asked to do it, they'd a said, 'Under no circumstances whatsoever.' I view that as a sign of progress," McCain tells Pelley.
"You mentioned in an interview that General Petraeus sometimes goes into Baghdad in an unarmored Humvee, and that there were neighborhoods you can walk though without being concerned for your safety," Pelley asks the senator.
"There is no unarmored Humvee, obviously that's the case," McCain says. "I'm trying to make the point over and over and over again that we are making progress. There are signs of progress. But it's long and it's hard and it's tough."
"You were a little annoyed with yourself, I think," Pelley remarks.
"Of course I'm going to misspeak and I've done it on numerous occasions and I probably will do in the future. I regret that when I divert attention to something that I've said from my message but you know that's just life, and I'm happy frankly with the way I operate, otherwise it would be a lot less fun," McCain says.
He's worried that the market misspeak is distracting from his conviction that the strategy is working after years of mismanagement by the Bush administration.
McCain describes former Secretary Donald Rumsfeld as one of the worst secretaries of defense in the history of the country. Asked why he says so, McCain says, "Well, the war was just very badly mismanaged, there's ample evidence of that."
"But the secretary of defense is not commander-in-chief," Pelley remarks.
"No, he's not," McCain agrees.
"What responsibility does the president bear for this?" Pelley asks.
"Again, I think the president has great responsibility for it, the buck always stops there," McCain says.
"But you seem to give President Bush a pass even though you are so hard on how this war was managed you don't seem to criticize the president for that," Pelley says.
"I say that he is responsible and I'll continue to say he is responsible. Should I look back in anger or should I look forward and say 'Lets support this new strategy, support this new general, and let's give it everything we can to have it succeed,'" McCain replies.