Some schools interview slowly (umich, Columbia...probably more but these are the ones I know about because I applied there) and a post-December invite gives the same chances as an earlier one. But most schools you have a smaller chance
As baronen26 mentioned, it varies a bit by school. Some schools begin interviewing later so your chances post-Dec 1. are still very good. For others, most spots will be filled by then so you're chances aren't too great at that point.