In the 10 years I have owned DVC, there was one time out of many times that I called last minute where I did not get a room, and I was looking for a room for Spring Break week & I called about 3 weeks prior.
Other than that, I have always gotten something. Now, that doesn't mean that I decided 1 week before the F&W Festival started at Epcot that I wanted to stay at an Epcot view room at the BCV and got it, but I have always gotten something.
It has been my experience that if I call last minute, I generally end up at OKW or SSR, because they are the largest resorts. I also usually put myself on the waiting list for another resort if I want something different. A couple of years back I booked at OKW and waitlisted BWV during th F&W Festival, and BWV came through the day before we left.