The polls found in Florida and Virginia, Obama leads Romney by the same margin, 48 percent to 44 percent of registered voters surveyed, NBC reported.
In Ohio, Obama holds a 6-point lead, 48 percent to 42 percent. The results include voters who are unregistered but leaning toward one candidate.
Romney has narrowed the margin since polls taken earlier this year, and Obama fell short of the 50 percent share considered a safe margin for an incumbent president.
Majorities in all three states said they believed the worst of the economic woes had passed but 40 percent or less said they believed the economy would improve in the next year.
Romney held a narrow lead among men in all three states, the polls show, while Obama had double-digit leads among women.
The polls found majorities in the three states -- 58 percent in Virginia, 57 percent in Florida and 55 percent in Ohio -- said they believed the country is on the wrong track.
The three polls were conducted May 17-20 and all have a margin of error of 3 percentage points. The Florida poll is based on responses from 1,078 registered voters; the Ohio poll, 1,103 registered voters; and the Virginia poll, 1,076 registered voters.