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Mr. Romney pushed back Wednesday, vowing to eliminate the rule that “compels religious institutions to violate the tenets of their own faith.”

“We expect these attacks from President Obama and his liberal friends. But from Newt Gingrich and Rick Santorum, it’s a clear indication of desperation from their campaigns,” said Ryan Williams, Romney spokesman.

In many ways, social issues never completely faded away. The candidates have argued that Roe v. Wade, the Supreme Court ruling legalizing abortion, should be overturned and have argued in favor of a constitutional amendment defining marriage as between one man and one woman. Aside from Rep. Ron Paul of Texas, the fourth candidate in the race, the candidates have fawned over the idea of appointing judges to the bench that are cast in the same mold as Supreme Court Justices Samuel Anthony Alito Jr., Clarence Thomas and Antonin Scalia and Chief Justice John G. Roberts Jr.

Religious leaders have struggled to coalesce around a single alternative to Mr. Romney, whose commitment to pro-life issues and traditional marriage have been long doubted by social and religious conservatives — including a small slice of whom are simply unwilling to vote for a Mormon.

But Marjorie Dannenfelser, president of the Susan B. Anthony List, a leading anti-abortion political action committee, predicted that Mr. Santorum’s stunning sweep of one primary and two caucuses Tuesday would shake up the 2012 campaign.

Santorum has the upper hand right now” among social conservatives, she said. “Social-issue voters really are the motor for campaigns. They will stay up all night, be on the phones all day, and they don’t give up.”