The survey, by USA Today and Gallup, indicated that the president owes this advantage mainly to a huge shift of women to his side.
In the fifth Swing States survey taken since last fall, Obama leads Romney 51 percent to 42 percent among registered voters.
A month ago the president trailed Romney by two percentage points, USA Today noted.
The biggest change came among women under 50, the report said. In mid-February, just under half of those voters supported Obama. Now more than six in 10 do while Romney’s support among them has dropped by 14 points, to 30 percent.
The president leads the former Massachusetts governor 2-1 in this group, USA Today said.
Romney’s main advantage is among men 50 and older, where he leads Obama 56 percent to 38 percent.
But Republicans’ traditional strength among men “won’t be good enough if we’re losing women by nine points or 10 points,”
Sara Taylor Fagen, a Republican strategist is quoted by the newspaper as saying.
“The focus on contraception has not been a good one for us – and Republicans have unfairly taken on water on this issue.”
In the poll, Romney leads among all men by a single point, but the president leads among women by 18.
The swing states surveyed were Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin.
The survey, taken March 20-26, had a margin of error of plus or minus four percentage points.