paying the hospital before delivery ?

So I haven't started paying for my delivery yet . I changed insurance company's this month. So I went from having a 5,000 deductible to 1,000. Not my hospital has called saying my delivery will cost 1,488 to me which sound great compared to before . Well they just left me a voicemail saying it has to be paid by my 7th keep month of pregnancy. My question is if it is not completely paid by then ? What happens they refuse to deliver my baby ?