If you plan to stay over New Year's, DO NOT wait until your final checkout day to call! Say you're staying Dec. 30-Jan. 4 (checking out the 5th). You'll want to treat each day as it's own separate reservation in order to get all the nights you want. If you wait until the end, chances are VERY likely you won't get anything prior to the night of Jan 1st. As I said, this is called "day by day" calling and member services is quite familiar.
For this hypothetical reservation, you would call member services at 9 a.m. eastern time on January 31st and book the night of December 30th. Tell them you're planning to call for several days to book more and they will mark this in the reservation. Then, at 9 a.m. eastern time on February 1st, call and book the night of December 31st - this will be the most critical one to get, so be sure to call RIGHT when they open. Again, tell them you've made one reservation already and that you'll be calling for more. They may at this point link your first and second nights, or they may wait until the end - I'm not sure. Then, at 9 a.m. eastern time on February 2nd, call and book the night of January 1st... and so on and so on until all your trip is booked. On the last call make sure they've linked all the reservations together into one and you're done!
It sounds confusing, but you'll most definitely need to do this to get in this time of year anywhere on property. The days after January 1st will be less crucial, but once you're in the day by day calling mode it can't hurt to continue. You may be able to wait until a little later than opening to call on those later days, but I'd still call day by day just to be safe. And don't let this scare you - there are very few circumstances where you have to make your reservation in this way. Most times you can do just as you planned and call the last day of your trip to book the whole thing with no problem. Christmas/New Year, Easter week(s), Grand Villas at the Boardwalk and standard views at the Boardwalk are about the only other resrvations you have to do this for.
Oh, and don't be leary! The folks at member services are terrific and will be happy to help you out any way they can!