Medical debts are a form of unsecured debt that can be dealt with in bankruptcy. This means that health care providers and those who are collecting medical debts (if the debt has been sold to a collections agency or if the doctor or provider is using a collection agency) are often going to be amenable to debt settlement.
Debt settlement is a process wherein you get a creditor to agree to allow you to make a payment that is less than the actual total that you owe to him. The creditor - in this case the health care provider- opts to do so because they believe that otherwise they may end up getting less or even getting nothing (if you declare bankruptcy and wipe out the debt with chapter 7). So, the first thing you will need to do is to make the creditor afraid they aren't going to be paid. Unfortunately, this is done by stopping your payments. If they are getting paid, they aren't going to have any incentive to work with you. When you stop your payments, you do have to be aware your credit is going to suffer. However, this is still a better alternative than bankruptcy.
Once you aren't making payments, make an offer to the creditor to settle the debt for less. Your lawyer can help you to decide on an appropriate amount, and can help you to draft the offer. Typically, you have the best chance of having your offer to settle accepted if you can arrange to make a one time lump sum payment of the amount you are offering, so be aware of that fact when considering how to settle debt.
Your lawyer will guide you through the entire process, and you should ideally be able to save quite a bit on your debt and avoid bankruptcy. If you do not already have a lawyer, you should strongly consider getting one before negotiating a settlement as you have the best chance of success with a professional on your side.