Voters turned a skeptical eye toward conservative-backed measures across the country Tuesday, rejecting an anti-labor law in Ohio, an anti-abortion measure in Mississippi and a crackdown on voting rights in Maine.

Even in Arizona, voters were close to turning out of office the chief architect of that state’s controversial anti-immigration law. State Senator Russell Pearce, a Republican power broker and a former sheriff’s deputy known for his uncompromising style, came close to conceding the race Tuesday with a look of shock on his face.

“If being recalled is the price for keeping one’s promises, then so be it,” he said. His opponent had declared victory. Mr. Pearce, the president of the Senate, was a hero to the Tea Party movement, and apart from his anti-immigration efforts, he had introduced numerous bills to nullify federal laws.

Taken together, Tuesday’s results could breathe new life into President Obama’s hopes for his re-election a year from now. But the day was not a wholesale victory for Democrats. Even as voters in Ohio delivered a blow to Gov. John R. Kasich, a Republican, and rejected his attempt to weaken collective bargaining for public employees, they approved a symbolic measure to exempt Ohio residents from the individual mandate required in Mr. Obama’s health care law.