Corker’s lukewarm support for Blackburn is more than an annoyance: The center-right coalition he represents is critical to Blackburn’s prospects in the race. But Chamber of Commerce-type Republicans are generally fond of Bredesen and his past stint as the state’s governor, seeing him as a pragmatic get-things-done kind of pol, as opposed to a hard-edged conservative ideologue in Blackburn.

“He’s a person that would get things done,” Tom Cigarran, a former Corker donor and chairman of the Nashville Predators hockey team, said of Bredesen in an interview Wednesday. “Marsha Blackburn, not so much.” Cigarran, who credited Bredesen with revitalizing downtown Nashville and reforming Medicaid, is backing the former Democratic governor and said people in his social and political circles are, too — “unless they are far-right fanatics.”

There are others. Colleen Conway-Welch, the widow of prominent GOP fundraiser Ted Welch, held a fundraiser for Bredesen in February. And Autozone founder Pitt Hyde, a reliable Republican donor from Memphis, is considering supporting Bredesen, according to two GOP sources familiar with the talks. Hyde did not return a request for comment.