Read the Fair Debt Collection Practices Act online. It details the rules of debt collection. Phoning and writing in an effort to collect the debt aren't "harassment." You have the right to tell them not to phone you at work. Request in writing that calls to your home stop.
If you received the services for which they are seeking payment, you do owe it. If you cannot pay for it, contact the hospital and request that they either settle for less or pay for it out of their charity budget.
Debt is debt regardless. Since the debt is unsecured try and send a minimal amount each month and stick with it. If they see that you are trying and ont ignoring the debt they will leave you alone. Whenever you can pay more do so as you may need to go to the same hospital again.
Technicaly they can harrass you. However it doesn't really help then since people will typically be more willing to work with a creditor if they don't come off as holstile. However it still stands that you have a debt with them and they will do everything they can to collect that debt from you.