U.S. President Barack Obama has weighed in on Mitt Romney's leaked remarks, telling one late night TV talk show host that, to succeed at America's top job, "you have to work for everyone, not just for some."

Obama made the remarks during a taping of the Late Show with David Letterman on Tuesday night.

"One thing I've learned as president is that you represent the entire country," he said, telling Letterman that he does not believe Americans are "victims."

It was Obama's first public response to the video of Romney, recorded in May and posted online Monday, in which the Republican presidential candidate is recorded sharing an opinion of Obama supporters.

"There are 47 per cent who are with him, 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. That that's an entitlement," he says in the leaked video clip.

Watching the political fallout in D.C., CNBC chief Washington correspondent John Harwood said the gaffe plays into the image Democrats are painting of Romney, as rich and out-of-touch with average Americans.

But Harwood told CTV's Canada AM that, given the relatively small number of swing voters expected to decide the presidential vote, the time Romney's devoted to the aftermath is potentially more damaging.

"Even if it doesn't move a lot of votes ... it takes time away from Mitt Romney, with just two weeks before the debate, in a time when he's behind President Obama and needs to make up ground."

According to the results of an The Associated Press-GfK Poll conducted on Sept. 13-17, Obama is supported by 47 per cent of those who expect to actually vote and Romney by 46 per cent.

Among likely voters, just 17 per cent were undecided or said they might change their minds before election day.

Harwood said that's what makes it so tough for Romney to account for his remarks.

"It's hard for him to apologize, because so much of what he said in that gathering tracks the policy agenda that he has for the campaign, and the basic arguments the conservatives are making."

In that light, Harwood pointed to a potential upside for the Republican hopeful.

"The thing that could keep it from being complete disaster," Harwood said, "is the idea that it would, in fact, energize his own people to hear him saying that at a private fundraiser."

Even before the controversy erupted over his remarks , Romney had acknowledged the damage such slip-ups could wield.

His own father, Michigan Gov. George Romney saw his own presidential aspirations dashed after he said his support for the Vietnam War came during an overseas tour where generals and diplomats influenced him with "the greatest brainwashing that anybody can get."

He quit his campaign in the furor that ensued.

Obama acknowledged he’s not immune either, telling Letterman that voters understand presidential candidates will make mistakes on the campaign trail.

During his 2008 campaign, Obama got into hot water when he was caught on video recorded at a private fundraiser, belittling small-town Americans.

Romney and Obama will have their first chance to square off in a debate Oct. 3.

There will be a total of three presidential debates and one between Vice President Joe Biden and Republican nominee Paul Ryan before election day on Nov. 6.