Where are you planning on being on Christmas Day? Is it a park day for you?
I just popped in December 25th on Disney Dining's reservation page, using a party of 4 for 6:30 pm, and multiple locations came up with availability. Perhaps not your first choices (and times were all over the board (from 5:05 pm to 8:30 pm) but definitely still some options to choose from.
We are doing the all-day dining at SeaWorld on Christmas Day. Our dining experiences (Santa's Fireside Feast, Dine with Shamu, character breakfast at the Polynesian, Shrek Feast at Gaylord Palms, and dinner at T-Rex) were all scheduled for different days besides Christmas itself so we can have less running around on a day that's bound to be packed.
If it were me, I would try calling T-Rex (located in Downtown Disney) to see if they might still have a table availab.e Looks like a cool place to enjoy a holiday meal. They often don't show up online but will have space available if you call them directly.