Disneyland has record crowds on Thanksgiving day. Your best bet is to get there when the gates open ride rides until it gets unbearable for you, then have lunch out side the park, nap/swim at the hotel, and return in the evening. You can get a lot done in the first few hours and I have also heard that if you get fastpasses and pass your window of time, the CM's will still let you in the fast pass line. So you may want to get some fast passes before you leave for lunch and use them in the evening, but if the park is that packed they may be out of FP's or the window may be several hours away. Remember, you can get a fast pass for Pirates and still get a fast pass for a different ride because Pirates isn't hooked to the "system".
You could also spend some time in DCA if DL gets too packed. DCA always has less crowds. And also, DCA and DL fast passes are not on the same system, so you can have a FP for a DL ride and a FP for a DCA ride.
The plus side of going that time of the year are the longer hours, less of the rides are down for scheduled maintence, and most of the eateries are open. Don't forget to make your reservations 30 days in advance for any sit down places in DL, DCA, hotels and DD.
I would say the Monday and Tuesday would be the less crowded days, just because many people may take the rest of the week off for a long weekend.
Enjoy the little touches of the park, use fast pass, and swim/nap in the afternoon, enjoy Downtown Disney and DCA. You will have a good time.
