A new poll shows President Obama with a slight edge on GOP challenger Mitt Romney in three key battleground states, with under a week left until Election Day.

A new Quinnipiac University/New York Times/CBS News swing-state poll finds Obama up by 5 points in Ohio, up 1 in Florida and up 2 in Virginia, but the president’s margin in the two Southern states has shrunk amid a Romney surge.

In Ohio, the poll finds Obama leading with 50 percent support from likely voters to Romney’s 45. The race is unchanged from the same poll released Oct. 22, which also showed the candidates at 50-45.

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In Florida, Obama’s 53-44 lead over Romney in late September has been trimmed to a 48-47 advantage. And in Virginia, Obama’s 51-46 edge over Romney in early October is now a 49-47 lead for the president.

“After being subjected to what seems like a zillion dollars’ worth of television ads and personal attention from the two candidates reminiscent of a high-school crush, the key swing states of Florida and Virginia are too close to call with the election only days away,” said Peter A. Brown, assistant director of the Quinnipiac University Polling.

Still, Obama holds a strong edge among those who have already cast their ballots, topping Romney by 50 percent to 44 in Florida, 60-34 in Ohio and 57-38 in Virginia.

Ohio voters give Romney a net unfavorable rating, with 48 percent unfavorable to 46 favorable. But in the other two states, voters view him more positively, with Florida voters giving him a 48 favorable and 47 unfavorable split. In Virginia, Romney has a 49 percent positive and 46 negative rating from voters.

The president is viewed favorably by voters in all three states, with a 51-46 split in Florida, 52-44 in Ohio and 52-46 in Virginia.

Voters in Florida (49-48) and Ohio (50-47) approve of the job Obama is doing as president. But voters in Virginia are split, with 49 percent approving, 49 disapproving.

In Florida, Romney is backed by independents by a narrow margin, at 49-44. Florida voters gave Obama higher marks, however, on which candidate better understands their concerns. Sixty percent said Obama cares about their needs and problems to 38 percent who said the president was unconcerned. For Romney, 47 percent said he cares to 49 who said he didn’t.

In Ohio, Romney has 49 percent support among independents to Obama at 43. Ohio voters said the nation’s economy is improving by a 40-30 percent split. Fifty-two percent of Ohio voters said their state’s economy was improving as well.

In Virginia, Romney takes independents by 57-36 and voters say the economy is improving by 40 to 35 percent.

The latest Quinnipiac swing-state numbers come as national and battleground polls show Romney and Obama locked in a tight race.

A national New York Times/CBS poll showed Obama edging Romney among likely voters with 48 percent support to 47 for the GOP nominee.

The Quinnipiac survey was conducted from Oct. 23-28 and has a 3-point margin of error.