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Relaying Mr. Obama’s reaction, White House spokesman Jay Carney said the president described the DOMA ruling as “historic” and the Proposition 8 ruling as a “tremendous victory.”

The rulings, though, were not complete victories for Mr. Obama’s stances. The court did not decide whether same-sex marriage is a constitutional right or address whether the California law is unconstitutional.

“They made an argument in the Prop 8 case; it was rejected,” Mr. Winkler said. “They made an argument in the DOMA case; it was rejected. So they are happy with the results of today’s cases, but their arguments were not accepted by the court.”