We just went during the 1st week of December & had been there in 2004 during the same week. Both times we just winged it & had no problems making same-day reservations with guest relations in the parks for the following:
Sci-Fi Dine In (11:30 lunch)
Liberty Tree (2:00 lunch)
Bistro in France (9:00 dinner)
San Angel Inn (11:30 lunch)
Jiko (7:30 dinner)
Rain Forest Cafe @ AK (11:30 lunch) - made no reservations at all
Wolfgang Puck Cafe - no ressies, walked up for 8:30 dinner
Mesa Grill @ Coronado (9:00 dinner) - walked up at 6:30 pm
California Grill - 9:00 dinner - Booked what we thought was a Monday night reservation on Sunday, got to Contemporary Monday night, guest relations turned out to have booked reservation for Tuesday. CM at Contemporary went ahead & fit us in for only 1/2 hr later so we would not have to come back on Tues.
In 2004 we also had no problem booking the night before for the Poly Luau, which I've read is normally a 90-day out reservation.
Keep in mind - it was the value season, and it was just my husband & I, so we were fine eating dinner that late. It gave us time to go back to our hotel, rest a bit & clean up. Naturally for larger groups or those w/ young kids who need to eat at particular times, it will probably be more difficult to find the exact time you want if you wait until the day-of. We also made Guest Relations our first stop at each park, usually arriving when the park opened - the exception was for the Bistro & Liberty Tree which we didn't try for until 11 am.
Also be aware that places you'd expect to be all booked up by the day-of (Cinderella's, Le Cellier, Crystal Palace), were. I think the Bistro is typically one of these too & we just lucked out because of the time of year. I'd definately recommend advanced reservations if you're looking to dine at one of those.