I'm not sure about right now, but I do have experience with this at Disney.
Back in 2003, my family had been having a bit of a bad time. I had lost my job and didn't work for a year, then only part time for another year and a half while I went back to college to get my degree in Information Systems. I was scheduled to graduate at the beginning of December of 2003. My dad died in September of 2003, and my wife's mother and step-father (now ex step-father) decided to spend Christmas away from the rest of the family at their timeshare in Orlando. Now, we live in suburban Jacksonville, so it's not like it's far, but with all of the other things that we had been through, that was a big blow to my wife...Christmas without her mom. Well, good things started happening. I did graduate from college, then my employer, who originally was a co-op with the university, offered me a full time job, which I started the second week of December, and I had an idea. So, the week before the weekend before Christmas (like 10 days before Christmas), I called Disney on a whim to see if they might have a room, just for a night, so we could at least see her mom the weekend before Christmas...and they did! They had just opened the Pop Century the week before we stayed there, and it was great! Not only did they have room, they had Florida Resident discounted rooms, and we only paid $49 for the room. It was awesome. We didn't go to any parks, since we were only there for one night and one day, but we did go to Downtown Disney, and had breakfast at 'Ohana...again, I got that reservation like three days before we were to show up.
I have heard that if they don't have something available, just call shortly before you want to do whatever (hotel stay, meal reservations, ect) and they MAY have an opening due to cancellations. It worked for me!
Kevin
Kevin