Breathe, you are not the first person to ever lose or have your passport stolen. Freaking out will not fix, find or do you any good but cause added stress. If your plane leaves the next day at 1 pm or after you should be completely fine.
Remember to always send your self a picture of your flight itinerary, drivers license and passport to your email and phone.
First thing is to Google the U.S. Embassy or consulate to obtain the address of the nearest one to you. If they open at 8am I would suggest being the first one there by showing an hour early. Better to be the first one in first one out.
Second bring with you a copy of your drivers license, picture of passport and airline or train Itinerary.
Third does it cost? It will not in most places cost anything for a temporary passport that will only last a year and to get you home. Wait to get a replacement after you get home which will cost $140 for your new one. Some won't cost if you have been a victim of a violent crime or a victim of a disaster.
It normally takes 4-6 weeks but not in an emergency situation like you have a flight to leave. I have had this situation like this happen and it will make anyone panic but there really is no need to.