As someone who is responsible for putting together my unit's schedule, I can certainly sympathize with the position your manager is in. I know at my hospital, it is quite a lengthy process even getting new positions posted, not to mention actually finding someone to hire.
If you signed a contract saying you were available to work up to 72 hours in a pay period, then your manager should be allowed to schedule you for those hours. However, there needs to be some middle ground here since you're obviously unhappy and thinking of leaving. You should talk with your manager and try to come to an agreement. Lay it on the table and let her know your thoughts. Any smart manager will try to make a good employee happy. Perhaps you could work 3 days one week, and 4 the next.
Good luck. I hope everything works out for you.