I actually own an ATM company and believe me its not easy to remove a stuck card from a machine, although it does depend on the machine.
The teller can open the machine, as it is most of their daily jobs to balance the ATM, but that depends on the bank as well. She probably wouldn't know what to do anyway.
I would just bitch and make them call a tech on the spot. There are techs in every city, and most of them have on-call contracts with banks and ATM owners. There's no reason to wait that long unless they have some sort of issue with your card.
