Bredesen is far more likely to face a challenge from a Democrat than a Republican, I should think.
Either way he's beatable
Bredesen pretty much has all the major Democrats snookered. Only State Senator Steve Cohen is beyond his grasp. Cohen is easily the most liberal member of the senate, but also has one of the best working relationships with GOP members of the legislature and has picked more than his fair share of fights with the Governor. I'd say he's the most likely Dem to make a primary challenge, but I doubt he would at this point.
Sen. Majority leader Ron Ramsey or Sen. Mark Norris would be perfect GOP candidates, but both have disavowed interest. Barring some surprise, Rep. Beth Harwell may be our last best hope.