Hint from my experience last year. If your local store is open on Thanksgiving night go then! If you go late enough you'll still get the Christmas sales prices but there are zero crowds.
My wife and I went last year and were expecting madness, there were more cashiers then there were customers :)
I almost always shop at Walmart in the evenings. It is such a nice experience if you don't mind the stocking activities. That may be why I don't share the complaints of other Walmart shoppers in regards to dirty, overfilled stores.