White House spokesman Jay Carney issued a statement saying Obama "congratulates the people of Ohio for standing up for workers" to defeat the measure.
Obama faces the challenge of appeasing his party's traditional base, which includes unions, while at the same time pulling in moderates and independents to win re-election.
Mike Thanasiu, 44, of Toledo, said it was unfair to force changes to existing union contracts, especially those covering firefighters and police officers.
"What they already have shouldn't be taken away," he said. "They do an invaluable service for us."
Kasich, meanwhile, said he respected the voters' decision and would spend time reflecting on the result. Ohio Republican Party Chairman Kevin DeWine criticized Democrats for not offering an alternative plan to deal with revenue shortfalls.
The vote certainly is a boost to beleaguered unions, which have been on the defensive all year as GOP lawmakers around the country sought to rein in budget deficits by targeting generous union pensions and benefits. Even Democratic governors in New York and Connecticut faced down their public employee unions to hold down costs, but did so without trying to limit collective bargaining rights.
Unions fell short earlier this year in their recall campaign to wrest control of the Wisconsin Senate from Republicans. A similar defeat in Ohio "would have been a calamity to them," said Gary Chaison, professor of industrial relations at Clark University in Worcester, Mass.
"This will be seen as a successful defensive action, but you can't win games just by stopping touchdowns," Chaison said. "The unions have to be careful that they don't try to read too much into it."
Associated Press writer John Seewer in Toledo contributed to this report.
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