Don't pay any place extra to expidite your passport. Just apply at your local post office and have them do a rush service. On your application they will actually ask you when you are leaving and what flight you are on. To rush the service with the government. On the governemtn website is states:
Expedited Service - Add $60 for each application
Each application is $82 PLUS the cost of the two pictures you need to submit with the applications... then add on the expidited fee if you need it.
Here is the website for the passport agency and application: http://travel.state.gov/passport/get/first/first_832.html
Here is the government page for "Rushed Passports":
http://travel.state.gov/passport/get/first/first_831.html
Finally, here is the link so you can find the closest place to submit your application- be aware that some places one accept application on specific days of the week and during certain hours- make sure you go when they will accept your application:
http://iafdb.travel.state.gov/