Also this page that does talk about appointments says this:
"If you have urgent travel plans and need to replace your passport immediately, you may walk-in to the Embassy in Madrid or the Consulate General in Barcelona during the following hours, except on U.S. or local holidays: For Madrid: 8:00 am to 11:00 am, Monday thru Friday. Emergency passports will be printed in 24 hours and will be ready for pick up the next day between 8:00 am and 11:00 am. For Barcelona: 9:00 am to 13:00, Monday through Friday."
I understand that you are able to make an appointment within your travel time frame, but I don't want to worry others in your position.