“My overriding goal is to be a participant in those Republican debates,” he said in an interview on Wednesday. “I need to start early.”

But Mr. Karger is hardly a political neophyte. He worked alongside the famed Republican strategist, Lee Atwater, to derail Michael Dukakis’s 1988 presidential campaign against George H.W. Bush. He was an outspoken critic of the Mormon Church for backing the 2008 ballot measure outlawing same-sex marriage in California. The liberal magazine Mother Jones described Mr. Karger as one of the G.O.P’s “top dark-arts operators” in a profile last spring.