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“I think Newt has consistently put those in, let’s say, the back of the bus,” Mr. Santorum said Sunday on ABC’s “This Week.” “He has never really been an advocate of pushing those issues.”

Mr. Santorum, Mrs. Bachmann, Mr. Perry and other candidates lagging in Iowa hope to pick up Mr. Cain’s supporters.

Mr. Cain, at one time a front-runner in the Republican presidential race, appeared Saturday in Atlanta with his wife at his side to announce the suspension of his campaign. He cited distractions caused by accusations - all false, he insists - of inappropriate sexual behavior and a 13-year extramarital affair.

He also said he plans to remain a strong, influential voice within the Republican Party.

Mr. Cain indicated that he will endorse one of his former rivals, and some have speculated that Mr. Gingrich ultimately will garner his support. The two took part in a 90-minute Lincoln/Douglas-style debate last month, and Mr. Gingrich released a statement Saturday praising Mr. Cain and his contributions to the race.

“He elevated the dialogue of the Republican presidential primary,” Mr. Gingrich said. “I am proud to know Herman Cain and consider him a friend. I know from having worked with him for more than a decade he will continue to be a powerful voice in the conservative movement for years to come.”

Mrs. Bachmann is among the candidates who are wooing Mr. Cain’s supporters.

“Our office had call after call after call from people who wanted to switch over and come and support me because people realize I’m the true tea party candidate in the race,” she said. “I think we’re going to pick up a lot of the support from across the country, people who formerly supported Herman Cain.”