We are going to be arriving Tuesday, January 20th and leaving Tuesday, January 27th. My birthday is during our visit, too, on Sunday the 25th! Woo-hoo!
I may be way off on this, but even if every room on property is full because of the 4/3 deal (and I know that isn't the case, as resorts that show no availability for the 4/3 deal show availability for rooms without the deal), that 33,000 rooms times I'm guessing an average of 3 people per room? That would average out to about 25,000 per park, which still isn't that bad.
If I had to guess, I'd guess that it will be a little busier than a normal January, but not uncomfortably so.
Or maybe I'm just being naively optimistic!