Just because Orbitz sold you a ticket...
...does not mean you actually got one.
I got the usual confirmation screen from Orbitz when purchasing a flight on Spirit. But upon arriving at the airport, Spirit had no record of the purchase.
Called Orbitz, they said Spirit never "responded" to their purchase order. The best Orbitz would offer was a refund. Gee, thanks.
I should have known something was up when the usual confirmation e-mail never arrived, but this was a last minute trip.
The lesson: If you don't get the confirmation e-mail, you probably didn't actually buy what you thought you bought.