In 2012, Martha McSally, a political novice, came so close to defeating her Democratic opponent, Representative Ron Barber, in Arizona that she flew to Washington for orientation and even appeared in the freshman class picture. She ultimately lost by fewer than 2,500 votes.
But Ms. McSally, a former Air Force fighter pilot and now a freshman Republican lawmaker from the district that includes Tucson, did not quit. She defeated Mr. Barber in a rematch last year, and now fills a seat once held by Gabrielle Giffords.