Mommy's progression into labor seems to have halted, not sure what to do.

So on Tuesday of last week my wife went to see the doctor for a regular visit and everything was normal and progressing fine. Today she went back for another visit and her progress seems to have stopped. Our 40 week due date is May 5th and the doctor wants us to think about when we would want to induce should she go beyond 40 weeks. I am sure that this is a just in case kind of thing, but with all I have read with induced labor to just so holidays aren't interrupted, shifts that were ending, or docotors just plain sick of waiting I am a tad paranoid when I hear doctors mention about inducing labor.

My question is it better to induce the child as close to the 40 week mark as possible to minimise any issues with having the baby in too long, or would it be better to wait the maximum time allowed to let God's design do its thing? This is something I haven't really read about or learned in the birthing classes. Any help or input would be appriciated.