Quinnipiac has Obama ahead of Romney by 45-41 percent in Florida; 47-38 in Ohio; and 45-39 in Pennsylvania.
"If he can keep those leads in all three of these key swing states through election day he would be virtually assured of reelection," said Peter Brown, assistant director of the Quinnipiac University Polling Institute.
Since 1960, no candidate has won the White House without taking at least two of the three states. Obama swept the trio in 2008.
Brown was quick to stress that the election was still more than four months away, "which is a lifetime in politics."
But the data suggests voters in the three states like Obama better. He has a net favorable view among Ohio voters, and his favorability rating is about even in the other two states.
Romney's favorability rating is negative in all three, Quinnipiac said.
In particular, voters approve of Obama's recent presidential action halting deportations of some younger illegal immigrants, according to the survey.
And the president's approval figures on the economy have improved slightly, drawing him virtually even on that front with Romney, a multimillionaire former venture capitalist who has touted his business acumen.
"For much of the last year, more voters in these swing states have said Romney would do a better job on the economy," Brown said.
"That advantage has largely disappeared, at least for now."
The poll's figures are somewhat more favorable to Obama than other recent surveys.