I've expedited through the US Passport office several times for various family members.

As I recall, you need a letter showing why you need to leave so quickly, a prepaid courier (e.g. FedEx) airbill and envelope, in addition to the expedite fee, pix, certified copy of birth cert, and application. I believe we photocopied our outgoing airline itinerary and provided that as well.

It took only a day or two in each case.