I have had this twice:
1) 'Plane was smaller than originally intended and when I got to the airport it was "£400 for volunteers for waiting until next day"
2) Business Class was overbooked - ironically the first time I had paid my own cash for Business Class. I was offered a downgrade to WT, which I declined. I flew a day later, and was upgraded to First at the gate.
So expect some problem, and prepare your helpful bargaining replies, E.g. "We are happy to go via BOS/PHL etc if upgraded", "We are happy to fly AA if upgraded", "We will accept compensation of £xxx if delayed a day" etc.