They do take walk-ins but I have no idea about the wait (I've never eaten there). My suggestions would be:
1) Keep calling until you leave. Cancellations do happen.
2) If you don't get one before you leave, call Disney Dining from your resort room. I've had success getting a PS that way for a meal I couldn't get before I left (called the morning I wanted it).
3) If you don't get a PS that way either, plan to get there shortly after they start serving.