Everything is booked... Amex tried that for us
If you can get a car and are willing to go to Chattanooga, it appears there are still rooms there.
Use the other travel sites Travelocity and Obits...you will get deal on line, I have worked in a hotels. They never gives deals when you call on phone direct to the hotel.
Tripadvisor shows rooms in Chattanooga and Birmingham. May be too far north for you though.