TALLAHASSEE (CBSMiami/NSF) — A new Washington Post poll shows President Obama leading Republican presidential candidate Mitt Romney by a margin of 51 to 47 percent among likely voters in Florida.

While that margin is not statistically significant, Romney needs to win in Florida, especially as another new Washington Post poll shows Obama leading in Ohio by 52 to 44 percent.

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Florida and Ohio are among the most-critical swing states in the election.

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The Post reported that Obama is benefiting in Florida from a double-digit lead among women voters — though Romney leads among men.

The newspaper reported that Florida voters, by a 60 to 35 percent margin, say they trust Obama more than Romney to advance the interests of the middle class. Also, Florida voters say Obama is more likely to empathize with people’s economic problems.

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“The News Service of Florida contributed to this report.”