Your best bet at this time would be to phone the nearest Italian embassy and request an appointment and explain the situation, fly to them and show them your tickets and see if they can expediate the process. They may be able to do something, perhaps not. You're welcome to try. Just make sure you have all the documents required and bring a few extra ones for back up. As for the usual processing times. Usually people say that to give them an idea on how long it will take to process a visa/application. They usually take a bit less time. No one in their right mind says "same day processing" (especially in government) because then you get people demanding that they do it the same day and loitering around outside.