When I needed my passport quickly, I was told to go apply in person at the Passport Office in the Federal Building in Westwood*. (As opposed to, for instance, the Post Office.) I think I received it in less than two weeks and didn't have to pay any extra. Well, I didn't pay extra money, I paid in time spent waiting the gawd-awful long lines at the PPO.
*Obviously, if you're not in LA, you'd need to check where the nearest Passport Office is.
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