If it was an emergency situation why the berth that it was originally allotted was now not available I would be understanding - emergencies happen.
But, if not, then it would be a hard sell I think - I can't imagine how much longer this would take...
I was on a plane once flying from Hawaii back home. First we had an electrically problem and got held up over an hour - but hey who wants to be in the air with an electrical problem - not me. As soon as that was fixed we had to stop mid-taxiing as a passenger started to have a heart attack. Yikes - thank God we were not in flight.
People all over the plane were so mad - they were going to miss connceting flights and some were really getting vocal. I knew we may miss our flight, but really it was all beyond my control and nothing could fix it, and I couldn't be mad at either hold up.