My friend lost a passport on new year's day in Paris, with a very important business meeting back in the US the next day. We called the 24 hour line at the embassy, the duty officer grilled my friend for 15 minutes, and then said they would communicate to the airline (Air France, i believe) that they felt she should be allowed to board. She got to airport 3 hours early, and made it home.
I think there is a good chance, but no guarantee, it will work out.