No signs of labor - did you deliver naturally?

I'm a FTM at my appointment this week (almost 39 weeks) my doctor started saying baby was big, I hadn't dropped at all (sitting very high), cervix still closed and she's not seeing any progress at all. Have any of you ever had this happen and somehow still gone into labor??? It really has me down and she was saying she really didn't think I was going to go into labor on my own. She said we would talk at my next appointment about inducing me at 41 weeks, but even then she thinks I will end up having to have a c-section because I'm pretty petite and baby is getting bigger than she expected.