Growing up in North Alabama all I can say is Georgia, leave the Tennessee River alone!
The Tenn-Tom waterway already diverts a substantial amount of water out of the Tennessee basin and into Mississippi & Alabama. Given the thirsty populous of Atlanta, and North-west GA, one can only assume that once they get a pipe stuck into the Tennessee, they'll suck it dry!.
Here's the thing, the state of Georgia, and kick in Alabama for good measure, would benefit tremendously from a desalinization plant on Georgia's northeastern coast. Yes, desalinization is expensive (in the near term) but it is very cost effective over the long term when compared to the environmental damage currently imposed down-stream of GAs most thirsty markets.
I agree with an earlier post in that Georgia, and specifically the Atlanta Metro area, needs to make substantial steps toward effective, long-term water conservation. This should be a prerequsite for discussions concerning diverting water from other states into Georgia.
Now, concerning the Tennessee river. While the governor of TN (or rather the government of TN) is an important figure in determining the potential diversion of water from its natural course, the river flows from TN, into AL, back into TN and KY. In addition, the TTB waterway already diverts water into MS and back into AL. The point of this is that in order for water to be diverted into GA, the governments of the aforementioned states would need to agree.
Since there is a long running water dispute involving GA and AL, I'd say the next governor of GA would be wize to court the AL governor BEFORE talking with the TN counterpart.
Here's a radical thought - why not have the governors of the entire geograpical region south of the Ohio River and East of the Mississippi put together a pannel of civil and environmental engineers and urban planners (no politicians allowed!) who, in conjunction with the TVA and Army corps of Engineers could review the current situation, and project water demands under several different scenarios for say, the next 100 years, and then present their findings and recommendations.
Otherwise, Georgia's water problem solution lies not to the north, not to the west, not to the south, but to the east. It's best known as the Atlantic Ocean and the process that makes pottable water from it is known as desalinization.