1. They agreed on the price of the car with the salesman, but now they can’t borrow enough from the bank. They’re over a barrel because they’ll lose their deposit if they can’t come up with the rest of the money.
2. If I look for another job, the companies I interview with are going to want to check with my current boss. But I don’t want him to know I’m looking for a new job. I’m over a barrel.

Similar to: in a bind; in a fix; between a rock and a hard place; between the devil and the deep blue sea.