President Obama will likely need to carry a majority of those states to earn reelection.

The president will be favored if current trends hold; with Democrats and Republicans added into the survey results, Obama leads Romney 51 percent to 42 in swing states. That's the first time Obama has led his Republican challenger in a head-to-head match-up in key states, with Romney edging the president by 2 percentage points as recently as February.

But independents have swung strongly to the president's favor in recent weeks as promising economic news boosts his favorability — and the effects of a bruising Republican primary catch up with Romney. 

The movement has been especially pronounced among women. At the end of 2011, Obama trailed Romney by 11 percentage points among independent men and five points among independent women, but over the past two months, Obama has swung that to a one-point advantage among men and a 14-point lead among women.

Romney, meanwhile, has seen 11 percent of women who supported him defect, versus just 4 percent of men. 

Interestingly, that movement does not seem to be driven by the president's controversial decision to mandate employer-funded free access to contraception. Nearly six in 10 women said they were unfamiliar with the president's view on contraception, while those who did know the president's policies were evenly split on whether they supported it. 

Nevertheless, the poll illustrates that Mitt Romney will need to focus his efforts on winning back the independents that were key to his early support — and who will inevitably swing the results of November's election.