Sometimes there are deals available a few days before. Check Expedia. I don't think I've ever encountered a deal through Disney itself that was available on such short notice, with one exception: an Annual Pass room-only discount that I was able to get on one day's notice several years ago. It's possible that that kind of discount might still exist on short notice, but I have no solid evidence that it does.
Most of the special deals that Disney offers have to be booked by a specific date, usually well in advance of the actual stay.
But it doesn't hurt to ask! One could have a PIN code that the reservation system knows about but that you don't know about.
HTH.