I only know the laws for MI, they may vary in your area.

If a patient is voluntary and wants to leave before the docs say so, they cannot leave before 72 hours. After that time there they set up a court case for the patient to argue that they are competent and of sound mind not suicidal, etc. and for the docs to say they need to stay longer. This can take up to another week in which the patient is kept in the hospital. Then the court makes their decision, and it goes from there.

Really, through that process you'll probably be in the hospital longer than the average stay (5-10 days) anyways and will only bring more misery for yourself. Tell them to stick it out and hope for the best.