Yes, they do, but you must leave a credit card confirmation. With this, you must cancel 48 hours in advance so your CC won't be charged $10 per person for a no show. This is for any holiday including Christmas Eve, Christmas, New Years Eve, New Years Day, Easter, Mother's Day, Father's Day, Memorial Day, Labor Day and 4th of July.
Also, please note that at this time, many places are already booked for Christmas Eve, Christmas Day, New Year's Eve and New Year's Day, especially if you happen to be looking for a traditional Christmas Dinner. You may have to go off the beaten path to find PS's that are available... some are:
All Star Cafe at the Sports Complex
Olivia's at Old Key West
Boatwright's at PO-R
Shutters at CBR
The Mayan Grille at CSR
The Plaza Restaurant in Magic Kingdom
Akersaus in Norway in Epcot
Good luck and have a happy holiday!
Hope that helps!