I didn't look into my insurance plan because it was not necessary. If your insurance doesn't cover or only cover certain number of sessions, you might have to pay out of your pocket. The state budget is a big problem. I don't think there is too much you can do.
If you child only has speech delay but no other signs of PDD/Autism, you might not need to be TOO worried. If it turns out he needs a lot of intervention but your state can't provide free service to him, you only choice is to pay out of your pocket or move to a state that has more budget for educational program like EI. I know this is probably not possible. Good luck to you and your family.