Hopefully somebody with practical knowledge will jump in here and answer your questions.
In the meantime if you do need a short notice passport, and assuming you live in or near Miami (based upon info in your post), there is a US Department of State passport agency in Miami.
You'll need two passport photos of the baby (you'll probably have to hold him in your lap - that's what we did with our newborn daughter when we got her passport).
http://travel.state.gov/passport/abo...ncies_910.html
The Miami Passport Agency only serves customers who are traveling, or submitting their passports for foreign visas, within 14 days. To apply at the Agency, you must schedule an appointment by calling toll-free at 1-877-487-2778, 24 hours/day.
And at some point you may want to look into what it will take for your son to obtain dual citizenship.