The commander in chief made the comment during his first joint appearance with his wife, Michelle, on the daytime chat program in New York.
The first couple taped the interview Monday and it aired Tuesday, the same day Obama addressed the U.N. General Assembly.
"Well, you know, first things first here," Obama said as the "View" hosts asked him what his post-White House plans were. "There's all kinds of things I want to do in the second term -- putting folks back to work, making sure our schools are up to snuff. We've got another war to wrap up."
"And then?" "View" panelist and producer Barbara Walters queried.
"You know, in a post-presidency, the thing that I think I would enjoy most is spending time working with kids," Obama said. "I love teaching, I miss teaching, and you know, I'm not sure it would necessarily be in a classroom, but the idea of being able to go around in various cities and helping to create mentorships, and apprenticeships, just giving young people the sense of possibility. ... Something along those lines, I think I would really enjoy doing."
Asked by Walters if a Romney presidency would be "disastrous for the country," Obama replied: "America is so strong and we have so much going for us. We can survive a lot. But the American people don't want to just survive. We want everyone to thrive. We want folks to have a shot at success, and so the question then just becomes, whose policies are more likely to lead us to where we want to go?"
Noting he, a Democrat, and Romney, a Republican, have different strategies for improving the economy, Obama said he thinks the key to turning the economy around will be the middle class.
"Governor Romney on '60 Minutes' was asked, does he think it's fair that he pays a lower tax rate than somebody who's making $50,000 a year? And he said, 'Yes, I think it's fair and I also think that's the way you get economic growth. The notion being that if people at the top have more income, they'll invest and they'll create jobs," Obama said.
"I've just got a different vision about how we grow an economy. I think, Barbara, that you grow an economy from the middle out, not from the top down, and that when the teacher and the bus driver and the receptionist and the office manager -- when they've got a little money in their pockets, when they're doing well, then that means business has more customers, that business makes more profits, they hire more workers, and that's been the history of our country, we grow fastest when the middle class is doing well and when folks who are trying to get into the middle class have ladders of opportunity. So, that's a different vision about how we move the country forward, and ultimately it's going to be up to the American people to make the decision about who's got the better plan."
Pressed by lone conservative "View" co-host Elisabeth Hasselbeck about whether his policies have failed the middle class, Obama pointed to his bailout of the U.S. auto industry, declaring it is "back on top."
Describing Romney as "a good man who means well," Obama said, "The policies he's putting forward are precisely the policies that got us into this mess."
The discussion also touched on the recent attack at the U.S. Consulate in Benghazi, Libya, that killed four Americans, including Ambassador Chris Stevens, which Obama said was an example of the very real dangers that still exist in the world.
"That's why we have to maintain the strongest military in the world. That's why we can't let down our guard when it comes to the intelligence work," Obama said, adding that based on the kind of weapons used in the Benghazi assault, authorities believe "it wasn't just a mob action."
He stopped short of categorizing it as a terrorist attack, saying the incident is still under investigation, but he emphasized the United States would not "shrink back from the world" because of the attack and would "hunt down" those involved.
"We will bring them to justice," he promised.
On a lighter note, Obama joked about being "eye candy" on the female-powered program and presented Walters with a gift basket filled with White House-themed goodies in honor of her 83rd birthday.
The president also recalled how he and Michelle met when they were both working at a Chicago law firm, how they shared their first kiss over ice cream sitting on a curb and how Michelle forgot their first wedding anniversary.