These States are Michigan, Florida, North Carolina, Ohio, Virginia, Colorado, Nevada, New Mexico, Iowa, Pennsylvania, Wisconsin and New Hampshire.
According to the poll, the Republican leader has taken a lead over Obama mainly because he has eliminated the lead the latter had over him among women voters.
The two are now tied at 48% among women voters, while Romney leads by 12 points among men.
Obama Campaign immediately disputed the poll results.
The latest Gallup/USA Today Battleground survey showing Obama and Romney tied with women in battleground states (48-48) is an extreme outlier, defying the trends seen in every other battleground and national poll, the Obama Campaign said in a memo.
"This result underscores deep flaws in Gallup's likely voter screen," it said.
According to the memo, only two years ago the distortions in Gallup's likely voter screen were exposed, leaving Gallup's survey nine points off the mark just days before the election.
"Gallup's likely voter model predicted a 15 point advantage for Republicans, 55-40, on Oct 31, 2010. The final result was a six point margin, 51-45. That year, Gallup's registered voter survey was much closer to reality at 48-44," the memo said.
In the past, Gallup's justification for such outlying numbers is that they are providing a snapshot of voter attitudes during a particular time period, not predicting the outcome of the election, the memo said.
The USA Today/Gallup Poll released on Monday showed Romney leading Obama 50%-46% among likely voters in the swing states. Men who are likely voters back him 54%-42%.
Romney pollster Neil Newhouse termed it as encouraging movement.
Meanwhile, another poll conducted by the Pew Research said that the voters are divided as to who will win today's presidential debate at the Hofstra University in New York.
"On the eve of Tuesday night's second presidential debate at Hofstra University, voters are divided as to which candidate they think will do the better job: 41% say Obama will do better, while 37% expect Romney to prevail. This stands in stark contrast to expectations prior to the first presidential debate two weeks ago, which voters expected Obama to win by a 51%-29% margin," the Pew Research said.