January is a busy month, Rpsemont.
You have the end of the Holiday/New Year's week when people are still on vacation.
You have the Marathon week after that (sometimes overlaps NY week).
You have MLK weekend which is a three day weekend for many folks.
You have locals that book campsites for weekends when the booking window opens at 500 days because January is cooler obviously and thus nicer camping weather than summer (when you can get weekends closer to time). That means that weekdays are often available but not weekends.
You have the snowbirds/retirees who book for long periods of time (some times an entire month) in January to escape colder northern climates.
Of course you can keep trying and people can and do piece together a reservation. Settle on a level of campsite and a timeframe then look for individual nights. You find a night (or two) here, a night there, and keep plugging away till the gaps are filled. People have done that successfully but you have to check often (every day and/or multiple times a day). You pay a deposit of one night which means on a one-day reservation you are pre-paying. Then before you arrive you can get the individual reservations merged into one reservation (same level, consecutive nights) which makes it easier for planning and dining (if you want to).
It's work but that's how it's done at this point. With increasing demand, no added extra campsites (Disney has added LOTS of hotel rooms over the decades), you have to book WAY in advance. As team bradfield said, (at least) a year in advance. And at the booking window for major holidays like Halloween, Thanksgiving, Christmas, and Easter seasons, you have to book at the max window. Sadly, it is what it is.
So it's up to you if you want to try to pull it together piecemeal (and obviously check for your entire stay) but odds are you'll be luckier with individual nights than one big chunk of dates. But cancelations do happen.
Good luck, Anne.
Bama Ed
PS - As an example, I booked Thanksgiving 2022 (2 weeks) at the Fort at the max booking window time which was about a month ago. Now (a month later) only Tent sites show any availability for Thanksgiving week.
PPS - Another example, the booking window is based on your ARRIVAL day. So I could be looking for a weekend (2 nights) in January but if someone books a month long (30 day) stay and leaves on that desired weekend, they have a 28-day head start on you on being able to get that weekend.