Among Letterman's theories: Obama said yes without thinking about it, or as Letterman put it, "Like Bush did with Iraq."
But Obama had other ideas. It turns out he was listening when Letterman had bantered with a woman in the audience who brought -- yes -- a potato in the shape of a heart to the show.
Obama told Letterman: "The main reason I'm here? I want to see that heart-shaped potato."
The woman tossed the potato to Letterman.
She agreed to let Obama keep it. Said the president: "This is remarkable."
Obama also had his most irreverent answer yet on the question of whether some of the vitriolic reaction to his health care plan is driven at least partly by racism.
"First of all, I think it's important to realize that I was actually black before the election," Obama said to huge laughs from Letterman and the audience.
Responded Letterman: "How long have you been a black man?"
Letterman covered a number of topics with Obama -- many of them serious -- in a taping that ran about 40 minutes. The show will be broadcast on CBS on Monday evening.
On the war in Afghanistan, Obama said he knows some people want him to bring troops home, and others are calling for him to increase U.S. force levels to combat the insurgency. The top U.S. commander there is warning the war could be lost without more troops.
Obama said he won't make a decision on sending in more troops, though, until he completes a comprehensive review of the war effort and settles on his next strategy.
"I'm going to be asking some very hard questions," Obama said.
Obama's visit made him the first sitting president to appear on Letterman's program. He had been on Letterman's show five times before, though, most recently in September.
The White House said it was a good way for him to reach yet another audience as Obama wraps up a blitz of TV appearances, trying mainly to build support for his health care plan.
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