Former Sen. Connie Mack told Dick Cheney he did not want to be Bush's VP
From the Washington Post's preview of Dick Cheney's forthcoming book, In My Time:
Later, Bush asked Cheney to lead his vice presidential search. Cheney writes that “it is harder to find a good vice presidential candidate than you might think,” adding that “everyone has negatives.”
Sen. Connie Mack (Fla.) told Cheney that he did not want to be considered, and Cheney discloses that Donald H. Rumsfeld, who would later become Bush’s defense secretary, was briefly on the list of possibilities. Finally, Bush turned to him.
Book overview here.