Call the school and ask if this tardiness disqualifies your application.  If not, explain your predicament to a reliable person and ask (beg) him/her to write for you in the next day or two.

In (legitimately) pestering for a letter from someone who's already late, you run the risk of them sending one that's either (a) rushed and terse out of resentment, or (b) dripping with unearned praise out of guilt.

Plan B: call your recommender and ask them to be honest: can they help you out, as they promised?  If not, please let you know now.

2014March:

This exact same thing happened to me, so you're not alone. It's been really agonizing not hearing anything back from a recommender. I called the specific school I was applying to and they were understanding.I'm still trying to reach my recommender to figure out what happened, especially since I am asking for recommendations to other schools. 

Best of luck. 

A similar situation occurred with me, where I was getting within 3 days of my deadline and my professor wasn't responding. However, he still came through for me as promised. The big reason that a lot of professors may be AWOL right now is because of Finals. Almost all arch schools are undergoing finals week right now, and my professor told me that he will sit down and do all of my recommendations the day after finals, which is what he did. If they promised you when you sat down with them, then they will come through for you.

It's happened to me twice. Contact the administrator at the school, explain the situation, and ask them if they will accept a late letter, and if you can communicate to the professor  when they will begin circulating applicant files for review. let your recommender know the outcome of that discussion, and begin looking for a backup in the meantime.