Giuliani notes "realistic problems" of 2012 run

Former NYC Mayor Rudy Giuliani on CBS' "Face the Nation."

Former New York City Mayor Rudy Giuliani said in an interview on "Face the Nation" that he is still thinking about running for president, but that he understands the "realistic problems" he'd have winning the Republican nomination in 2012.

Giuliani, who was known as "America's mayor" following the 9/11 attacks being commemorated on Sunday, ran for the Republican presidential nomination in 2008, but he didn't gain traction in any of the early voting states and left the race soon after. He has said he is considering another run, but some of his more moderate positions, especially on social issues, could be a obstacle for him to win votes from Tea Party supporters likely to vote in the Republican caucuses and primaries.

CBS News chief Washington correspondent Bob Schieffer asked Giuliani about his current thinking about a presidential run in an interview tied to the 10th anniversary of 9/11. He confirmed he was still thinking about a second bid, but "not today."

"I'm gonna sort of put my thinking off for a couple of weeks until I get over the emotion of this... and see where everything stands," Giuliani said. "I understand the realistic problems I'd have getting nominated. So I have to take that into consideration. And around 9/11 I don't like to think about politics as much."

In the interview, Giuliani recalled what he was doing when he first heard about the attacks on Sept. 11, 2001 and the moment that he says "changed all of my emotions"

"I was having breakfast at the Peninsula Hotel about six miles from here, Midtown Manhattan. And I was told that a twin engine plane had hit the north tower and that there was a bad fire here. So I didn't know how bad it was until I actually got here. About a mile away I saw a big explosion, the second plane. I knew it was a terrorist attack," he said. "And when I got basically over there, I can see it where I was. I saw a man -- throwing himself out of the 100th floor... That really changed all my emotions."

"That said to me this is much worse than anything we've ever faced before and we're gonna just have to do the best we can. That's when I really knew how bad it was. But it wasn't... until I actually got here and I saw the planes and I saw people throwing themselves out of the window that -- my -- my goodness, this is the worst that we've ever faced. And we just better pray to God that we can do the right job," he added.

Giuliani also told Schieffer about what happened when there was a report that Giuliani had died at Ground Zero. He said he was trapped in a building two and a half blocks away, along with the deputy mayor and the police commissioner, while waiting for a call from then-Vice President Cheney when the the first World Trade Center tower came down and knocked out the phones and shook the building "like an earthquake."

"And we were trapped there for about 20 or 30 minutes. And people couldn't reach me and that's why they thought... we had been crushed with that first building," he said.. But then we got out... we had to go through a basement, through an underground passage."

Giuliani also told of an event that sticks out in his mind in the evening of 9/11 that he called "one of my best moments that day."

"I was standing up north there and I saw all these big men walking toward me. And they weren't firefighters, weren't police officers. They were construction workers. And I went up to one of them, I said, 'What are you doin' here?' He said, "We came here to pick things up because we're big and we can help." I said, 'Well, you can. You're just gonna have to put hats and masks on.'" he said. "About 300 or 400 of them just walked in... And then eventually turned out to be about 1,000. And it made you feel like you weren't alone."

"And that was true of the whole country," Giuliani added. "We got tremendous help from Mayor Daley in Chicago. He sent Chicago police officers here. We got tremendous help from Governor Bush in Florida. He sent Florida State Police here. That was real important. I think the people of this city felt alone and isolated and the rest of America embraced New York. And I think that helped us get through it."

When asked if he thought 9/11 changed the country, Giuliani said it did "mostly in good ways."

"I think it made us more realistic about the threat that we faced. I think we have much better intelligence today. I think spiritually we're stronger... We were attacked with the worst attack in the history of this country and we survived it," he said. "And the city is bigger, stronger... twice as many people live down here now as before September 11th. So the terrorists thought they were gonna destroy this place, this place is twice as big as it was before. So we showed a lot of resiliency that we need to remind ourselves of. And we had a tremendous unity."

But he added he wished that unity could also apply to other challenges facing the U.S., like the economy.

"I wish we could apply some of that to some of the other things we face, which are almost as big. Our... economy is now a national security issue, not just a debate about one ideology or the other, it's hurting our national security because our economy is so bad," he said. "Well, we should get over being Republicans and Democrats and think as Americans and get it solved."

Watch the full interview with Giuliani