I hope you don't eat your words. Yes, there are alot of rooms at those resorts in total. But those inexpensive rooms are in high demand...for those booking last minute, those wanting to extend their stays, and those wanting to check in a day early. Also consider the number of those rooms that may be booked for hurricane evacuees or those traveling with a sports group. Not to mention the possiblity that there are refurbishments going on, therefore rooms unavailable for booking.
I in no way think it is completely impossible, but I wouldn't gamble on it. I booked a 2 bedroom villa at OKW weeks ago, with the expectation that the BCV would never open up. I checked a few days ago, and was able to switch my reservation. Granted, I was able to change to what I really wanted, but that was after securing my second choice just in case because I knew that I wanted a room that night. I guess it depends on the flexibility of the OP with regards to where they stay.
***BTW, the Food and Wine festival begins this weekend, also
MNSSHP. I think that will contribute to room availability or lack thereof...IMO.***