Normally, for an expedited service, it takes 2-3 weeks to receive your passport from the date you applied, so if it didn't arrive at that time, you may request a refund by writing to:
U.S. Department of State
2100 Pennsylvania Ave., N.W., Washington D.C. 20037-3202
Put the passport number (if available), name, date and place of birth, application date, mailing address and phone number where you can be reached.
Only the expedited fee of $60 will be refunded. The regular application fees and your overnight delivery costs, if any, won't be.
Need to know exactly how to apply for a passport in a hurry? Click on this link.
The government's passport agency has been harshly criticized for massive delays in processing passports as a result of the surge in applications due to the new security laws passed by Congress, but I actually got lucky when I applied earlier this year. I got it only 5 weeks after applying. Not a bad wait at all, I was told. When I applied, the clerk at the post office said I should expect it in 12 weeks.
On a related note, if you want to help ease the backlog, you can apply for a Passport Specialist job. Here's a link to that job posting. The pay looks so good it might make you (almost) forget your passport application woes.