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Aside from a failed legislative bid in 2004, the Kansas-raised Mr. Miller had no experience running for office before jumping into the race to take on Mrs. Murkowski. He is friends with Mrs. Palin and her husband, Todd, and they both endorsed him.

Mr. Miller also had the blessing from tea-party activists. The California-based Tea Party Express said it spent nearly $600,000 to help Mr. Miller — most of that in the race’s final weeks, when Mr. Miller’s camp said it sensed momentum was on its side and that Mr. Miller could win.