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When it comes to unifying the GOP’s uneasy factions, Mr. Shirley adds another name, South Dakota Sen. John Thune, who has credibility with the political right and, like Mr. McDonnell, not likely to take the spotlight from Mr. Romney. “Nobody votes for vice president,” Mr. Matthews said. Mr. Thune’s drawbacks: He hails from a tiny state and has no major legislative accomplishments to his credit.