I got offered a trip to Munich in 10 days last fall and I didn't even know where my copy of my birth certificate was. If you go on the us site:
How to Get Your Passport in a Hurry
and do a little research, you can get this done in one day provided the location isn't too far away. You need to call the 1 800 number and schedule the appointment, get there with all your identification, and pick it up later that day. It worked for me, no problem