My understanding is that the United Nations General Assembly takes place at this time, starts the 18th, and many people are in NYC for this. Hotels have no problem filling rooms.
Just won this Marriott location for two nights. Started at $80 for 4* in Westminster, it was rejected. Went to $90 and added Soho and won this 5* Marriott in Westminster.
If you want to stay in Times Square the re-bid zones you are looking at are some distance from Times Square. Not just in mileage distance but the types of areas you will be staying in. Try for Midtown East, Midtown West and Hell's Kitchen.