"I would say we've gotten to the point where people will evaluate the whole person," he said. "None of us, at least I don't think any of us, have perfect lives. I can say very credibly to people: 'Judge me by my public performance.' Whatever mistakes I've made in my personal life, I made -- I'm sorry for them."
He said he'd like to be seen as "somebody who, despite whatever was going on privately, was able to take a city from 'Crime Capital' to 'Safest Large City in America,' from 'Welfare Capital' to 'Best Welfare to Work Program.'"
And he is also the man who is remembered for getting New York City through the worst crisis in its history.
"In my case, maybe because there's a record of acting under pressure and acting in a crisis," he said, "maybe that's something they'll look to and they'll say, 'Well, that's the way we're going to make our decision.'"
Still, Rudy is having trouble keeping his personal life out of the campaign.
Earlier this month, his 21-year-old son, Andrew, told the media that he and his father were estranged and that he had a problem with his stepmother. Rudy has said this is a private matter and said his wife is not to blame for any estrangement with his children.
"This is my responsibility, not hers. She's done everything she can. … She loves all the children," he said.
And as for how he thinks his wife would fare in the White House, Rudy said, "Judith will be a wonderful first lady, because she loves people. That's the key to it. You've got to love and care about people."
The feeling is mutual.
"Rudy would be the best president of the United States. He is a man of incredible character and integrity and … and always has been," Judith said. "He is not only intelligent, but he has an intellectual curiosity, and so he always wants to learn about the world and other people. And that's … that's very important."
He also has, as Walters noted, "a wife who's crazy about him." And Judith agreed.
"That he does," she said, laughing. "That he does."