As others have said, GOOD COMMUNICATION is the key in any delay situation.

All it would take to calm down most pax is for the crew to advise about the reason for the delay, with their best estimate of the departure time. And regular updates if/when the situation changes. This won't make everybody happy, but at least it will quell much of the anger as they can at least understand what is happening.

I have seen crews that are great at this and can diffuse lots of potential anger...and crews that go on radio silence and cause the pax to get even more frustrated and angry (see OP).