If you go to the U.S. Department of State website, you can read all the information you need about getting a passport:
http://travel.state.gov/passport/passport_1738.html
It appears that there is something called a Gateway City Agency, which serves customers who are traveling within 2 weeks.
However, the specifics depend on the city where you live. If this is your first time to get a passport, then you have to go in person to the closest office. If you are renewing, then you could do it by mail, but it would probably be quicker to go in person if there is an agency in your hometown.
You can find your local office from this link:
http://iafdb.travel.state.gov/
They will probably have a phone number that you can call to find out how to get a passport in 2 weeks.
I hope this helps.
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