Slim to none. Or none to slim.
Even if you had a discount in the days leading up to that week, they are based on each night and there wouldn't be any room discounts for nights during Thanksgiving time itself. I'm not sure what day any room discounts stop in November (meaning whether it's the weekend before T-giving, or some day(s) in the week before T-giving) but it unlikely you would have a room discount around the holiday itself.
Edited - thought I would just add - I haven't been Thanksgiving, but I have been at Christmas. We had an AP room discount on 12/19 or 12/20 (it was the Saturday before Christmas) but starting the next day, everything was full price all the way through to New Year's.