Boy, that's a tough situation. I personally would not be comfortable having a baby without some kind of insurance plan in place. Insurance is for the unexpected, you know. What if, heaven forbid, the baby has complications and requires a long stay? Can you really afford that? That can run hundreds of thousands of dollars.
I can tell you this about my own DD who was born 2 years ago. I am very healthy, and she is very healthy. She was full term + 1 day. (That's a trait from DH's family- being a day late and a buck short.) My prenatal visits were covered 100% by my HMO, as were all the tests. I don't know how much that would have run, but certainly not cheap. I had to have 2 ultrasounds at outside facilities. While I didn't pay for those, I did get the EOB and each was just shy of $500.
The actual birth was probably about as easy as childbirth can be and it the final cost of birth + hospital stay was $17,000, not including the $2000 for an epidural- which would have been worth every penny even if I had to pay for it
. This bill did not include newborn care, but my HMO negotiates with the hospital to include newborn care in with mother's care as a packaged deal. My DD developed very mild jaundice and they wanted to be safe and treat her; they tried to bill us $1700 for that, the HMO told them to go fly a kite.
So for my simple and straightforward birth, it was more than $20,000, not including routine prenatal visits. My HMO paid 100% thank goodness.
An option for you might be a birthing center, but what happens if you go to a birthing center and are then directed to a hospital because of complications? What if she needs a C-section? I have no idea how much the costs can run on something that gets more complicated and requires a hospital. Even the healthiest mother in the world can't be assured that her baby won't be breech.
I don't mean to sound discouraging, but unless you have a pretty spectacular amount of money in savings (maybe you do), I would be cautious about having a baby without maternity insurance. Some private companies do offer maternity plans. If you can afford to pay cash for a baby, maybe a better use of your money would be to buy maternity insurance and hold off until it kicks in. The peace of mind alone would be worth it to me. Some states offer maternity plans, so that might be worth looking into- they would rather a woman have some kind of coverage to guarantee dr. visits, a safe birth, and a healthy baby that will not be a drain on the public system.
Good luck.