Obama speaks out on Romney video

(CNN) -- President Barack Obama suggested Tuesday that Mitt Romney was "writing off a big chunk of the country" in remarks made in the controversial, secretly recorded video from a May fund-raiser published Monday.

In an interview taped for "The Late Show" with David Letterman in New York, the president said he didn't know what his opponent was referring to in the video but was quick to add, "One of the things I learned as president is you represent the entire country. If you want to be president, you have to work for everyone."

"What people want to know though is you're not writing off a big chunk of the country because the way our democracy works," said Obama. "This is a big country. And people disagree a lot but one thing I've never tried to do and I think none of us can do in public office is suggest that because someone doesn't agree with me that they're victims or they're unpatriotic."

The secretly recorded footage exploded on-line Monday when the liberal-leaning news organization Mother Jones posted a story and video clips. Tuesday the web site put out an additional clip and then later in the day published more than 49 minutes of the recording. Among Romney's remarks that stirred controversy was a comment describing "47 percent of the people who will vote [for president Obama] no matter what" as being dependent on government.

The president continued noting the 2008 presidential race against Sen. John McCain.

"When I won in 2008, 47 percent of the American people voted for John McCain," Obama said. "They didn't vote for me and what I said on election night was: 'Even though you didn't vote for me, I hear your voices, and I'm going to work as hard as I can to be your president.'"

Letterman noted Obama's own campaign gaffe in 2008 when then-senator and Democratic candidate said at a fund-raiser in San Francisco that certain Americans will "cling to their guns and religion."

Obama said he "immediately felt it was wrong" and quickly apologized, compared to Romney who has defended the crux of his comments though admitting they were "not elegantly stated."

"There are not a lot of people out there who think they're victims," Obama said. "There are not a lot of people who think they're entitled to something."

Obama continued: "We've got some obligations to each other, and there's nothing wrong with us giving each other a helping hand so that that single mom's kid, even after all the work she's done, can afford to go to college.