Obama and Romney tied at 45 percent, whereas a head-to-head matchup last month had the president trailing 43 percent to 46 percent. Obama leads Newt Gingrich 46 percent to 44 percent in the same poll.

Still, the president, who won all 12 of those swing states in 2008, has a tough fight ahead of him if he hopes to duplicate that success in 2012.

Obama’s approval rating sits at 41 percent, with 52 percent saying they disapprove of the president’s performance. Those numbers are even worse among independents: 37 percent approve while 56 percent disapprove. Obama trails both Romney and Gingrich with independents, by margins of 3 points and 1 point, respectively.

Without the backing of independents, the president will find it difficult to recreate the energy of his historic 2008 campaign.

The Purple Poll covers Colorado, Nevada, New Mexico, Iowa, Minnesota, Wisconsin, New Hampshire, Ohio, Pennsylvania, Florida, North Carolina and Virginia. A USA Today-Gallup poll of the same states released earlier this month estimates that Obama will need to win half of those states in 2012 to win reelection.

Among the GOP field, the Purple Poll shows that Herman Cain’s recent troubles are catching up to him.

Following a string of sexual harassment allegations and foreign policy missteps, Cain has become a polarizing figure among Republicans in the swing states, tied with Texas governor Rick Perry as the candidate voters say they are most likely not to support.

In addition, only 28 percent said they had a favorable view of Cain, while 52 percent had an unfavorable view of him. Those numbers are even worse among women, with only 23 percent saying they had a favorable view of the candidate.

Cain made a couple of questionable jokes after the sexual harassment allegations against him surfaced. He referred to Rep. Nancy Pelosi (D-Calif.) as “princess Nancy” at a debate, which he apologized for, and said if his GOP presidential rival Michele BachmannMichele Marie BachmannTom Petty dies at 66 Bachmann: Muslim immigrants trying to undermine Western civilization Religious leaders pray over Trump in Oval Office MORE was an ice cream, her flavor would be “tutti-frutti.”

The poll also shows that Romney continues to struggle to win over the Republican base. Romney has the lowest favorability rating out of all the GOP candidates, at 42 percent. Gingrich leads the field at 56 percent.