Leave the US on an EU national identity card, that is. I doubt they'd know what that is.

On the other hand, the check at the airline counter is just to determine that you have the right to enter the country you are flying to (check).

The check at security is just to determine that you are who your ticket says you are (check). I have seen threads on this board trying to answer the question: will a national identity card from an EU country get me past security at a US airport? The answer seems to be: it depends.

But why would you want to exit the US on an EU national identity card? You had to show a passport (US or other) to enter. Why not show it to leave?

That said, it seems logical that you could leave your passport in your pocket and identify yourself with your national card (if the staff at the airline check in could read it -- stay away from Greek).

Good luck!