Feels like nothing is progressing

I'm pregnant with my first and today is my due date. I know a majority of pregnancies, especially first pregnancies, go past the due date, but it feels like I'm at a stand-still. I'm 1.5cm dilated and haven't had any contractions, bloody show, or anything. My doctor says that if he isn't born in a week then we'll schedule an induction, but I was curious to see how many other women had experienced this as well and how far after their due date they gave birth and whether or not it was with inducing.