Since it's a virtual lock every that two SEC teams will play in BCS games, there are enough bowls for 11 SEC teams. If more than 11 of the 14 teams qualify, a 6-6 team would be locked out, unless there are slots in non-SEC bowls that cannot be filled by the contracted conferences or at-large teams with more than 6 wins.
I figure that Arky, Miss. St., and UK will not qualify. Miss. St. has the best chance among the three, but if they go 6-6, we'd probably get invited ahead of them.
I think UT, Vandy, and UF all go 6-6, and the Liberty picks us, leaving the Compass and Independence Bowls to pick between Vandy and UF. The Florida bowl games obviously love having the Gators, but if UF falls below those games, a TN bowl will pick us before they'll pick them, because Gator fans will probably not be eager to leave sunny Florida to take a cold vacation watching their 6-6 team.