According to the State Department, you can get a passport "right now" if you have a life or death emergency.
This site advertises same day passports for "urgently departing citizens" but doesn't mention the life or death thing.
Can you get a same day passport, even if it's not a real, honest to goodness, emergency? The non-government website makes it seem like you can, but I guess that's a matter of interpretation.
The official requirements to get a passport at a passport agency are that you are "traveling internationally in less than 2 weeks or need to get a foreign visa within 4 weeks." You normally need an appointment, but at least some agencies are known to take walk-ins as an unadvertised policy, but you may be waiting a very long time. You'd need proof of your upcoming travel, such as a copy of your itinerary, but don't need proof of a life-or-death emergency.
There's no guarantee that it will be the same day though; they may have you come back the next day to pick it up sometimes, such as if you don't need to travel for a few days. But they will generally be able to get you a passport before your trip, barring any issues such as problems with your documents or verifying your identity.
