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A two-candidate runoff will be held April 2 if no one receives more than 50 percent of the vote.

On the Democratic side, Elizabeth Colbert Busch, sister of TV political satirist Stephen Colbert, is the early favorite to win her primary and presents a potentially competitive general election contest in a district Republicans typically dominate.

Despite Mr. Sanford’s past political successes, he faces an uphill climb just to emerge from the primary, said Bruce Ransom, political science professor at Clemson University in South Carolina.

“I don’t think he realizes how embarrassing that whole [adultery] episode was. He made the state a laughingstock of the nation,” Mr. Ransom said. “I think perhaps he does not recognize the depth of the disenchantment with him for what he did.”