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She adds: “Brown is likely going to have to outperform Obama, even if the president carries the state again.”

A Public Policy Polling survey of likely Ohio voters released on Nov. 9 found Mr. Obama leading all Republican candidates, including Mitt Romney, 50 percent to 41 percent; Herman Cain, 50 percent to 39 percent; and New Gingrich 51 percent to 38 percent.

The poll came out a day after Ohio voters repealed the state’s collective bargaining law, but PPP President Dean Debnam said Democrats should not be gloating as they look ahead.

“The electorate next year won’t be as friendly to Democrats as the one that showed in Ohio yesterday,” Mr. Debnam said in a statement.