I just did a search for Christmas Eve, since you cannot book until tomorrow w/o a reservation and everything is coming up mid-afternoon when I try dinner or lunch.
And it is mostly Tony's and Liberty Tree Tavern, but there is some scattered stuff for CP.
If you have a room reservation where you can book ten days out, I would book something ASAP for Xmas day and be flexible with your times. The parade is at noon and 3:30 pm, so you will have to work around that. Also, don't expect to be able to walk out of the restaurant and find a place to watch the parade - I would be at my spot fairly early.
If you cannot, get online as early as possible tomorrow morning when the window opens up for Xmas day.