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Missouri also became the first state to test the popularity of Mr. Obama’s health care overhaul law.

Voters strongly approved, by more than 70 percent of the vote, a new law that prohibits the government from requiring people to have health insurance or from penalizing them from paying for their own health care. That conflicts with a federal requirement that most people have health insurance or face penalties starting in 2014.

The legal effect is questionable, because federal laws generally supersede those in states. But its passage sent a clear political message to Mr. Obama and the Democrats.