I dont see how this could happen, unless you ordered your passport originally not knowing you were heading to the U.S in the coming month, and now you are caught without. Since the original paperwork when you file for a passport asks when your next travel is scheduled, and the recieving officer at the passport office also confirms this date when accepting the application.
If it was within a short window (Ie: Surprised with a last minute trip and needing a passport) you can pay the increased cost to have the emergency passport issued, which is a lot more, but gets it to you almost immediately.
Calling the office once you have filed, like you said wont help... since it aleady in the system and being processed in the order it was received in the office... did you not get a reciept with the ETA when you filed?
I would look at cancelling your trip... I know it sounds drastic, but chances are you are going to have problems... the passport rules have been in place for quite some time now, and airlines and customs officers are pretty strict about these type of things!