As the PP said, the odds do change depending on which month you're looking at...getting a
DVC villa in November for December, for example, would take some significant luck.
Another factor is the length of the stay you're contemplating...short blocks of time are more likely that longer ones. Your villa size also matters...one-bedrooms book up more slowly than studios, I've found.
But, even if DVC is "sold out" a month prior to your contemplated travel, people do cancel and last-minute trips are possible. It helps if you can be flexible on your dates, and/or if you are willing to change resorts (maybe multiple times) while you're there.
All three times that I've booked a trip on this short of a notice time frame, I booked a room on cash as "back-up" so I could buy my airplane tickets...all three times I wound up at DVC, but was prepared to pay cash had it not worked out. Once the trip was in March; once in January; and once in April. Twice I wound up with one-bedrooms; once with a studio.
Frequent calls helped me piece together those trips w/out a lot of "pain" in the logistics (couldn't do it in just one phone call, though...it did take multiple calls)--the W/L helped back in the day when you could do day-by-day W/L'ing; W/Ls haven't worked on short notice since the change to only two per use year, though.
Good luck.