Does the OP have Nexus? If so, I would just use that to go to the US while my passport was being processed for a visa.

Can you drive across to the US using an enhanced drivers license (Drivers License Plus in Quebec?), then fly from a border airport to where you need to go?

If not - you're in the same boat as I was when I needed an Indian visa. I couldn't forfeit my passport to the Indian Consulate due to travel, so I avoided India.