Not only possible but probable for quite some time. I would expect a few days here & there but to get anything more than 3-4 nights in a row would surprise me.
The first week of December is one of THE busiest for DVC. Typically, the entire resort is booked within days of the 11 month window opening. It is a small resort with only 295 units with a max of 428 (meaning if every studio & 1BR were booked as such & not combined to make a 2BR). We purchased at BLT specifically to be able to book that week.
It is possible you might get lucky and catch a cancellation around 31-60 days out - DVC turns over any units not booked by members to WDTCo at 60 for booking by general public & 30 days is the deadline for members to cancel without their points being sent into holding.
I would also try looking for 1-2 nights at a time OR the second week opens up a bit compared to the first.