OK, people aren't going to like this but here it goes. First of all, the answer isn't to put the responsibility of your child on the state. This is one good reason why we all pay high taxes, why our states and our country are in debt, and why medical procedures cost so much in the first place. Everyone else has to pay for the shortcomings of people who don't pay at all and people who use Medicaid which short-pays. If you were adult enough to make a baby then be adult enough to pay for it yourself. If you couldn't afford this baby then you should have made sure you didn't get her pregnant. Call that harsh, but you can't deny it's true. It's not everyone's RIGHT to have a baby. If you think it is your right then it should be my right to deny you any "assistance" to have it and take care of it. It isn't my responsibility, and my tax dollars shouldn't have to pay for it. Now, before anyone gets on their soap box, it's a different story if people go into a pregnancy and/or parenting situation and things change that aren't their fault (i.e. they get laid off, a spouse dies, a spouse gets sick, a special needs child is born, etc.). These people are deserving of state help. If you are low middle income with kids on both sides already then what are you doing having more kids?? I realize this was not your idea and I'm not actually trying to attack you personally, but am trying to make a rebuttal against people who actually do these things and people who actually promote it as an answer.
You shouldn't complain about $3500 to $10000. Ask them what your costs would be with NO isurance. And you can't add coverage thru Blue Cross - or any private insurance for that matter - now that she is already pregnant. That's like adding more car insurance after you have had an accident. It doesn't work that way. Trust me - my father has sold all types of insurance for the same company for 40 years, my sister is the Director of the Risk Management program at a well known University, and I have a concentration in insurance both in my under-grad and grad degree.
If you can save a good portion up before the baby is born often times hospitals will settle with you for a fraction of the actual amount owed if you can give them one bulk payment. For instance, if your total to the hospital is $10,000 and you call them and tell them you have $5,000 you can pay them that day if they will take that as payment in full many will do it. They simply write off the other $5,000 so it ends up only being a $3,300 loss to them - which probably isn't a loss at all considering how far they mark up their service costs to help cover the people I mentioned above - those who son't pay and those who have Medicaid. If you think about it you are essentially doing what large insurance companies do with hospitals and doctors - you are negotiating a price for their services instead of paying their full price. Do you ever notice on your Explanation of Benefits how it shows how much the doctor or hospital charged the insurance, and how much the insurance actually pays (and the hospital or doctor takes as full payment)? That's because insurances have negotiated amounts they will actually pay for services and treatments. For instance, say you were getting an ultrasound. If you paid for it out of your pocket you may pay $225 for it. If the insurance pays for it they may only pay $100. It isn't uncommon for the insurance to only pay 25-50% of the actual amount a doctor or hospital charges. So there isn't any reason YOU can't negotiate with them. This is very powerful knowledge that most people don't have, and they pay full amounts when they don't need to.
So what I am saying is by doing this with the hospital and doctors you can be responsible for yourself while paying the same an insurance company would instead of paying the full amounts and your bucks helping to make up for those people who don't pay or use Medicaid! It might take a little more work, but at the end if the day this baby is YOUR baby and you should jump on board to do some work to lower it's expense.
At the end of the day, you could always negotiate with them on the total amount and then tell them you'll have to do payments if you can't save up a large chunk. Let them know that you understand how insurance works and how they get to negotiate rates and you want to do the same, and after you do that let them know you want to make payments on that amount. They WILL work with you on it. They would rather get payments than nothing at all!
Your girlfriend may also consider getting a job somewhere that has group insurance. Even though she is already pregnant the insurance would cover her since group programs do not consider pre-existing conditions as exclusions for coverage. She would have to make sure she got enrolled in the insurance in the required time period (usually 60 days) or else she would have to wait for the annual "open enrollment period" all group insurances have so employees who didn't join during their initial 60 day period can get in on the program (this is USUALLY in October, but not always). But before all that happens make sure the employer actually carries maternity insurance on their plan. Not all do because it is quite an extra expense that ends up being paid by all on the plan. She may take a look at Starbucks - they used to offer insurance to even their part-time people. I don't know if it includes maternity though. This was back when I was in school and that has been 10 years now! (YIKES! lol)
I hope that helps, and I hope no one gets too pissed! lol