U.S. President Barack Obama says whoever occupies the White House represents the entire country — a rebuttal of his Republican challenger's recent characterization that nearly half of U.S. voters are “victims” dependent on the government.

Appearing on television's popular “Late Show with David Letterman” Tuesday, President Obama made his first public response to a secretly recorded video of Mr. Romney speaking at a private fundraiser in May.

In the video released Monday by the liberal magazine Mother Jones, the former Massachusetts governor is shown telling the audience that 47 percent of voters who support the president pay no taxes, but believe they are “entitled to health care, to food, to housing, to you name it.”

Mr. Romney said he is not going to “worry about those people.”

Mr. Obama said being president means “you've got to work for everybody, not just for some.”

The president's campaign has portrayed Mr. Romney, a retired multi-millionaire businessman, as out of touch with the real struggles of everyday Americans.

After the video was released Monday, Mr. Romney said his remarks were not “elegantly stated.” He said he was trying to highlight his differences with the president, whom he says believes in “a government-dominated society.” Mr. Romney said that he wants to help all Americans, but is convinced the president's approach does not do that.

But the video's release has prompted concerns among Republicans about the direction of Mr. Romney's campaign, especially after he came under harsh criticism last week for his response to anti-U.S. protests in Egypt and the deadly attack on the U.S. consulate in Libya.

Two Republican U.S. Senate candidates — Linda McMahon of Connecticut and Massachusetts incumbent Scott Brown — both issued statements Tuesday criticizing Mr. Romney's comments in the video.

Mr. Obama was embroiled in a similar situation during his 2008 White House bid, when he was secretly recorded at private campaign fundraiser telling donors that white rural voters angry about their struggles “cling to their guns or religion.”

Mr. Romney has begun falling behind the president in polling of likely voters across the nation and in several individual states where electoral votes are critical for each campaign.