In your case where you are traveling next day you should be eligible for same day pick up. Passports can be made in house same day. Please make sure to bring an acceptable passport photo, state issued identification, and citizenship (passport, bc, naturalization certificate, Citizenship certificate, etc.). Even if you have a application in process bringing these documents will speed up the process of approving you application.
It's very possible. My appointment was for the 4th and I flew out the 7th (SUN). As long as you have your credentials
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