You can get a passport issued in 24 hours... or even the same day I believe.... BUT you would have to make an appointment with the passport office in your city and have travel documents in hand to show them. Both Parents will need to be there.
Need a US Passport Immediately ...
You should make an appointment to be seen at a Regional Passport Agency only if:
The U.S. passport is needed in less than 2 weeks for international travel
The U.S. passport is needed within 4 weeks to obtain a foreign visa
Contact the National Passport Information Center to make an appointment or locate a Passport Agency.