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He struggled to excite them in the primary, thanks to his evolving position on abortion and concerns about his Mormon religion, which fed into a lingering skepticism among evangelicals about whether he is truly committed to their causes.

As a result, many voted for Rick Santorum, the former senator from Pennsylvania, who consistently touted his support of traditional marriage and pro-life stance on the campaign trail, helping him outperform Mr. Romney again and again in states where exit polls showed that more than half the electorate called itself evangelical or born-again Christian.

Even when Mr. Romney won the Virginia primary in March, thanks to the absence of Mr. Santorum and conservative rival Newt Gingrich, he lost at the ballot box on the campus at Liberty to Rep. Ron Paul of Texas, by a 60 percent to 40 percent margin.

“Santorum was this group’s preferred candidate in the primaries, and so far, there still isn’t much enthusiasm for Romney,” Larry Sabato of the University of Virginia’s Center for Politics said of conservative Christian voters. “Romney needs big margins in places like Lynchburg to overcome Obama’s margins in Northern Virginia and elsewhere.”

Mr. Obama’s announcement last week, though, has given Mr. Romney another chance to get conservative Christians jazzed about his candidacy.

“I think just that announcement has driven hundreds, if not thousands, of people to Mitt Romney or a lot closer than they would be,” said Zach Martin, executive director of the College Republicans at Liberty University.

Democrats on Sunday defended the president’s decision to embrace same-sex marriage. Sen. Dianne Feinstein, appearing on “Fox News Sunday,” said there was “no political calculus in this, because it’s not smart.”

“If he’s going to do it from a political point of view, it doesn’t make any sense,” she said.

Massachusetts Gov. Deval Patrick said the president acted on his convictions.

Mitt Romney has occupied many positions on many issues, and back in 1994 when he was running for the U.S. Senate, he said publicly that he would be better than Ted Kennedy on gay and lesbian issues,” Mr. Patrick said. “He takes a different position in front of a different audience today.”