If you have the email of the DO that would be great. whether you call, email, or whatever be patient. Tell the DO how well things have gone for you academically, MCAT scores, and how everything is in place(LORs from committee, primary app, and 2ndry app) and you are just waiting on the DO letters. Remind him the interview season is almost over and you have no interviews yet. Don't forget to wish Happy Holidays.
Ask if it can be done by Wednesday. Call on Friday to follow up. You need to create a tangible sense of urgency without being a jerk. skip sarcasm and jokes if it is email since that can be misread.
Also you may want to consider looking for a backup letter writer if it is not too much trouble.
I thought my DO letter was going to be the fastest but it turned out to take 3 months.