In addition, the poll put the president ahead of Mr Romney by 5% among likely voters polled across the nation. The poll had a margin of error of 3.6%.
'Israel's destruction'
On Mr Letterman's show, Mr Obama said he told the US on election night in 2008 he would work for everyone, including those who did not vote for them.
"One thing I've learnt as president is you represent the entire country," he said.
"There are not a lot of people out there who think they are victims" or simply entitled to benefits, Mr Obama said.
Mr Obama's rebuke came at the end of a day in which more clips of Mr Romney's fundraising address emerged. In one, Mr Romney said the Palestinians are "committed to Israel's destruction".
"The Palestinians have no interest whatsoever in establishing peace," he says in the video, adding that "the pathway to peace is almost unthinkable to accomplish".
But chief Palestinian negotiator Saeb Erekat told Reuters news agency that Mr Romney was wrong to accuse the Palestinians of not seeking peace.
"Only those who want to maintain the Israeli occupation will claim the Palestinians are not interested in peace," he said.
In another clip, the former Massachusetts governor is shown discussing Iran's nuclear programme, and warning that America itself could come under attack.
$50,000-a-head fundraiser
The first clips released on Monday showed the Republican candidate saying those who did not pay income tax would never vote for him.
Crazy Monday
Home & Away
Eve Woman
Generation Next
Sunday Magazine
