Registration opened up sometime in November. Honestly I doubt you have any chance at a Hotel Room this late in. I imagine a good chunk of people that registered the first day wont even get a room if they didn't get it done in the first few hours. I could be wrong, but seeing how Old Hotel Reservation System worked and the New Reservation System worked last year, I'm pretty confident with my assessment.
Your best bet is to find someone else that is likely going to have a room, or if you are willing to spend the extra cash go reserve a room directly with one of the Hotels in the area. There are a few Hotels within walking distance that don't partner with Fanime, and even Fanime partnered Hotels have a few rooms off the Fanime discounted list. If really desperate you could get a room further out if you have a car or are willing to navigate public transportation.
If you are for sure going regardless of if you can get a room or not (which I imagine will only fly if you are local or get a off-list room), then you might as well save the $10(?) for your badge now. If not, you can play wait and see if you find someone with a room and not risk the waited money.