NEW YORK — Barack Obama warned Tuesday his Republican foe Mitt Romney was "writing off a big chunk of the country" following his remark that 47 percent of Americans were "victims" and therefore backed the president.

Obama offered his first response to Romney's remarks, made in a secretly recorded meeting with rich donors, at a "Late Show with David Letterman" taping in New York on Tuesday, 50 days before the presidential election.

"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," Obama said.

"What people want to know though is you're not writing off a big chunk of the country because the way our democracy works ... this is a big country.

"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.'"

"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."

Romney said in the excerpts of the video published Monday by "Mother Jones" magazine that 47 percent of people were with Obama, "who are dependent upon government, who believe that they are victims, who believe the government has a responsibility to care for them, who believe that they are entitled to health care, to food, to housing, to you-name-it."

"These are people who pay no income tax ... so our message of low taxes doesn't connect," he said.

"My job is not to worry about those people. I'll never convince them they should take personal responsibility and care for their lives."

Watch the full interview below, originally uploaded to YouTube on September 18, 2012: