It's not IDEAL, but you still definitely have a decent shot at acceptance. Since you didn't provide any stats, I'll try and oversimplify this as much as possible:
Let's assume if you interviewed pre-Dec 1st you had a 50/50 shot at being accepted. All things being equal, your chance of being accepted with a January 28th interview are probably somewhere around 1/3 or 1/4 just because a large portion of the schools class will already be filled up by that point and therefore your competing for fewer open spots.