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Twenty-eight percent of those polled identified themselves as Republicans. Of the remaining respondents, 31 percent said they were Democrats, 33 percent were independents, and 8 percent said “other” or didn’t know.

The survey showed Mr. Obama with a 5-point overall lead on Mr. Romney in the general election — down from an 8-point lead in March, before Mr. Romney clinched the Republican nomination. Mr. Obama leads 47 percent to 42 percent. Eleven percent of respondents said they would vote for someone else, wouldn’t vote, or were undecided.

Still, Gov. Bob McDonnell, a top surrogate for Mr. Romney, said Thursday that it’s way too early to be reading any tea leaves for November, pointing to a Rasmussen poll released earlier in the week showing a dead heat in Virginia.

“There are different polls out there — the point is, none of them matter,” Mr. McDonnell said during his monthly appearance on WRVA radio’s “Ask the Governor” program. “Romney just finished a brutal primary, so of course his negatives are being higher. He’s still consolidating the base. We’re just starting the homestretch now of the presidential campaign, and I think it’s going to get better by the month for Mitt Romney.”