Has an Amnio started labor for any of you?

I have an amnio scheduled for the 7th of December.  I am a little nervous because she will just be shy over 37 weeks.  They tell me that it is to see if her lungs are developed enough for me to try the induction.  (IAM REALLLYYYYY NERVOUS ABOUT AN INDUCTION FAILING) and if her lungs aren't developed then we wait another week or so and have her c section.  They are telling me that the only way that I am going to try this vaginally is if I don't go over 37 weeks.