Interesting and confounding problem, and not uncommon.  I hope that it works out for you.

In general, I instruct students for whom I write LORs to email me twice a week in the last month before the deadline.  (Just a blank message with, e.g., "friendly reminder about Lamar's letter for Feb 1st" in the subject line is enough.)  They're reluctant, as most of us wouldn't want to pester someone from whom we're getting a major favor.  But it's a big help to me in keeping it toward the top of the pile.

I know this doesn't help in the present circumstance.  But if you find yourself asking for letters in the future, ask recommenders if they'd mind getting an occasional reminder in their inbox.

Good luck.

I message them to keep in contact a week before, then I send a reminder the day before and it usually works.

Whether or not it will affect your application will depend on whether the recommendations get there before the committee starts to meet.  In most programs this doesn't happen for a few weeks after the deadline - in the meantime the applications are mostly being logged in, checked for completeness, and preliminarily screened by clerical staff.  It's not unusual for rec letters to be missing, and for fall semester grades to still be unavailable or incomplete at that point, so those factors aren't counted as marks against the candidate early on (but any missing pieces that are in the candidate's direct control do usually result in points off or notes or whatever that school's system is for recording deficiencies.)

If your letters are still missing at the point that the application goes to the committee, it matters more, both because it will usually be flagged somewhere (some schools put coded stickers on folders for that sort of thing, or highlight the deficiencies in a summary or checklist) and of course because the reviewers won't have the letters to read.  A letter received at that point may never make it to the applicant's folder, because the folders are circulating among the reviewers, so it may just be too late. 

Keep in touch, and politely ask them to let you know when it's been sent.  If you're getting no response at all then consider asking someone else for an additional recommendation.  It won't count against you to have an extra letter, and it will help if somebody's arrives too late or not at all.

You know what you should do? Kick them in the penis. (don't do this)

Thanks a lot guys!

Actually, I am missing only one person's letter at this moment, not sure if it is too late right now. But I think I will aggressively follow up with the last person this weekend and see if it works.

Josh-

That is exactly what I want to do!