I wouldn't give up on it. I don't think it's "miserable" at all. You can go perhaps on Wednesday or Thursday (actual Thanksgiving day) and it should be fine. Fri-Sun would be kind of crazy -- maybe Legoland would be better.
We now have season passes to Disneyland so we see the park a lot. It can accomodate a tremendous number of people, now spread over 2 theme parks (CA Adventure is a big draw too). The rides have the fast passes so you can strategize which popular rides the kids want to go on, get fast passes each hour, and not wait in line for those rides at all. In addition, on busy days, they use all the "equipment" they have (on not so busy day, they run less boats/roller coaster cars, etc) so the lines are really not any longer than on a quiet winter day.
I wouldn't cancel. The weather is gorgeous and there is lots to do. It's 73 and sunny today! Katherine