My first son was 8 days late. I was induced with him 3 times before it finally worked. The reason for this was that my doctor was an idiot. She had my date wrong by at least 3 weeks. Lucky for me, she went on vacation after induction #2, or I would have had a c-section. Her father 'took over' for her while she was on vacation, and instead of a c-section, he sent me for a prenatal profile. I had already been induced twice, and the prenatal profile showed I was only 38 weeks then! I still had to be induced, but it was a week after my correct due date. I tried many things to get labor to start, and nothing worked.
My second son was 11 days late, and another one that I tried many things, with no success. At least this doctor had some sense, and let me wait it out. I went into labor naturally, just very late.
My third son was born on his original due date, which was the day before the date the doctor had decided was the 'official' date. The reason for him coming right on time (as far as I'm concerned) is that the doctor did a thing they call 'sweeping the membranes'. The amniotic sac is somewhat adhered to the cervix, so the doctor breaks this 'seal'. I've heard and read many cases where this helped to get labor going. Unfortunately, I don't think my son was actually ready to be born. I ended up being in labor for 4 days, and never really did have 'real' contractions. I barely made it to the hospital. I was 8 cm dialated and having bloody show when I arrived. The doctor said if my water had broken at home (or in the car), that's where I would have had him.
There is a reason all the books say that an 'on-time' delivery can be anywhere from 38-42 weeks: sometimes it just takes longer, and the doctors aren't perfect. The baby will come when she is ready to, and not a minute sooner!
I would recommend that you have a prenatal profile done before you make any major decisions, like induction or c-section. The prenatal profile checks to make sure the placenta is still working as it should. The prenatal profile could save you a lot of grief.
I know that being so close to your due-date, only to watch it go by and
still be pregnant is aggravating, but sometimes it really is for the best
Hang in there! The end is near!