Given a travel related situation, and given a specific question about the situation, summarize the question into a title

I have an international flight leaving early Tuesday morning. The visa agency has had my passport and application for more than 3 weeks, but due to problems with the photograph and embassy closures they will not be able to get my visa until Monday afternoon. The agency has offered to same-day deliver the visa as soon as they pick it up from the embassy. It's possible that if they can get my passport to FedEx or UPS by 3PM Monday, that it will arrive in the evening by 9PM. But should I call the airline and prepare for the possibility that my visa won't arrive in time? Or is it possible to arrange my visa to be sent to the layover airport (ORD) on Tuesday?
Waiting for visa to be express mailed one day before international flight