The landslide vote to repeal an Ohio law that limits collective bargaining has sounded a strong note of caution for Republican governors and lawmakers across the country, raising questions about some of their legislative efforts, especially those that would weaken labor unions. But the victory, while trumpeted by labor leaders, may not necessarily improve the prospects of unions or the Democrats, their traditional allies, in 2012, political analysts said.

As labor leaders took their victory lap Wednesday, Republicans and Democrats from Maine to Wisconsin were adding the Ohio results to their political calculus for next year’s presidential election. Would there be fallout in Wisconsin, where Gov. Scott Walker could face a recall vote next spring? What can Democrats do to try to keep the energy — and the issue — from fizzling?

Gov. John R. Kasich, who had pushed the law in Ohio, seemed chastened, acknowledging on Tuesday night that, for voters, the bill had been “too much too soon.” Even before the vote, his approval rating was just 36 percent, according to a Quinnipiac poll in October.

“The results here in Ohio are likely to give Republican governors and legislators incentives to be cautious,” said John C. Green, director of the Bliss Institute, a political research center at the University of Akron. “The popularity of the Republican position has fallen somewhat.”

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