Nearly every new health insurance policy written will have a "preexisting conditions" exclusion for any medical condition an individual currently has. Pregnancy would fall into this group. While it may be nearly impossible to find a standard insurance plan to cover the upcoming delivery, there are some options that are available.
Most states offer low-cost, affordable health insurance for individuals and/or their children (and this includes children within the womb in many cases!). In Indiana, we have a program called Hoosier Healthwise designed directly for low income families. Pregnant women can be eligible for full coverage or pregnancy coverage depending upon the family's income and assets. If you live in any other state, check with your state's government website.
Don't forget to check with an employer. You may be able to land a job that will provide health benefits before your baby is due. Most will have some sort of probation period, principally 30-90 days before you become eligible for benefits. And, be sure to inquire about any pre-existing conditions clause if you haven't had coverage in the past 12 months.
Do you belong to any trade associations or have any hobbies (cycling, homeschooling, small business, etc.)? Don't overlook these as an option. By pooling resources, many associations have been able to successfully arrange benefits for their members. It may be worth a look.
As a last resort, you may think about some type of point of service health program. These programs do not provide insurance "protection" but reduce the cost of health care services if the individual chooses to utilize the services of a provider in their network. Since they are not insurance products, they may not include an exclusion for maternity. Discounts range from 20-60%. While this option will not pay entirely for the delivery, it may be a cost effective non-insurance solution.
Finding a way to pay for this life-changing event can be difficult, but it's not impossible. Thinking outside the box is an important first step.