Train? Train? This is the US, mate. We don't believe in public transportation. :-)
I don't think the railroad runs that way, no. Checking on Amtrak's site, it insists that you'd need to take one of their busses along the route -- and that it would take over 3 and a half hours.
To check on trains (or in this case, Amtrak busses):
http://lb.amtrak.com/
To check on Greyhound busses:
http://www.greyhound.com
Greyhound seems to have a number of direct busses that take 2-3 hours. US bus stations are invariably in the worst part of town.
There are probably private company options available, but I haven't lived down south for years, so I don't know them.
(Edit for clarity.)
[This message has been edited by ebell (edited 07-30-2001).]