Children’s hospital saying they won’t accept the amount I can pay monthly??

My son was hospitalized with children’s hospital for 2 nights due to pneumonia. I have an almost $8,000 bill even after insurance. And don’t qualify for financial aide of course. I’ve tried to negotiate down the bill, they’re saying the lowest I can pay is $165 monthly or it will go to collections. I told them I’m wanting to pay monthly just can’t do that much. I know it will take forever to pay at a lower amount but I literally cannot do that much monthly. I don’t understand why they can’t just take what I can pay monthly and not send it to collections. A supervisor is suppose to call me tomorrow but I’m not sure what to do.