L., I skimmed over the first two responses you had and they seemed to have great advice about calling and negotiating with the hospital, especially if you don't have insurance. It seems that if you don't have insurance there are more options in terms of help paying off your medical debts than if you do have insurance. This is talking from experience because my kids and I have insurance while my husband does not. It is a lot of work but if you are willing to do the work you can save money in the end.
Now, if you do have insurance and they have paid to cover the bill you may be in a tighter spot in terms of negotiating the medical bill down. However, some offices want to keep you as a patient and resolve the debt (especially if its been a long time) and you can call and ask them if they can reduce your debt at all, for the most part they will counter with "we can take off this much if you pay off the rest right now" or they may give you a three month option for paying off the rest of the debt. I have found that honesty is the best policy, if you can only pay X amount towards this debt every month, then tell them that and hopefully they'll put you on a payment plan to pay that much every month and make a note of it on your account. Make sure when you talk to anyone that you document the date, time and the persons name. This is very vaulable when you call back in if you are having any problems.
Now, if you debt is with a small office (not the hospital) call the office directly and talk to the billing coordinator about your situation or see if you can talk to the doctor about it. I used to work for a chiropractor and helped with billing insurance, and there were a few instances where people fall on hard times and because the doctor wanted to keep them as a patient, and they took the initiative to call in BEFORE we sent them to collections, we would write off half the debt or all the debt.
The biggest key is to call them BEFORE they start calling you demanding the money. It doesn't matter who you are workign with, people will take it in good faith that you are notifying them of your situation and being proactive about your finances.
Good Luck! I know what you are going through as we are going through a similar situation. Times are tough for everyone.