We were there the 23rd - 30th, and it REALLY picked up after the 24th. Christmas Eve in the MK was fine, it only felt crowded in the mid-afternoon (we were in the Haunted Mansion within 10 minutes around 11:30, much quicker than I expected). Fast Passes were readily available that day. We spent Christmas day at Disney Quest (moderate crowd), and Christmas night in Epcot (moderate crowd there too...didn't go on any rides, just walked around the countries and had dinner/drinks/snacks). We heard that the MK was closed with capacity crowds by mid-Christmas morning. The crowd in Epcot on the 26th was noticably larger (though not by much), MGM on the 27th was miserable, Epcot on the 28th was very crowded (my sister waited 45 minutes for brats in Germany, though my mother claimed the crowd was not nearly as bad as the day before), and the MK was horrible on the 29th (by late morning, most Fast Passes were either for late at night or gone for the day).
We still had fun! I wouldn't have chosen the time of year to go, but it was for a special extended family trip. I'd love to go the week before Christmas and leave on the 27th, just as the crowds really get huge in all the parks.