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“I wouldn’t seek a constitutional ban for same-sex marriage, but I am pro traditional marriage,” he told Mr. Gregory.

In Mr. Perry’s case, the Texas governor says he supports the New Hampshire repeal. But in July he said that New York’s move to legalize gay marriage was “fine by me.” A week later, facing social conservative criticism, he walked back the comments.

“It’s fine with me that the state is using their sovereign right to decide an issue. Obviously gay marriage is not fine with me,” he said then.