What are your plans for Thanksgiving Day? When you call you can ask for the list of what is available for Thanksgiving. They will list all the restaurants and times.
Many of the restaurants will have extended hours so if you don't mind eating earlier, you should have some options left.
But, I agree with the previous posters, call as soon as you can. Even if you don't get your first choice, make an ADR for something else. You can always switch if your first choice becomes available. Thanksgiving week is a busy time at WDW. If you are planning on having sit down meals at the table service restaurants, you should make all of your ADR's asap!
We tried for CA Grill at the Contemporary, but they were booked. We decided on Jiko at the AKL since they will have regular menu items available (DH is not a big turkey fan).
Good Luck!