This happened to me for a professor who was writing a letter for an application due on December 1st. I called the school and they told me that applications wouldn't begin being considered until Jan 1, so I was able to relax.
But by now, if a school has a Jan 15 deadline, they are probably starting to read applications right away. I would look into getting a new letter writer if he doesn't respond because it would put you below people with complete applications. A professor would probably be understanding if they hear their colleague is not responding to any communication.