Several others have answered this fairly well, but I would like to add that we live by this concept called CCO or "Crew Critical Off" time. Based on the flight limitations of the crew on that flight, on that day there is a defined time that the flight must be airborne, or someone will exceed their crew duty limits.
Accordingly, CCO becomes the driving factor on whether or not we can operate that flight. If our CCO is 2204z, then we've got to be airborne at that time....period. If we can't get airborne by 2204z, we either don't leave the gate....or we have to taxi back to the gate and re-crew. It is really out of our hands on what happens at that point.....we either get the plane off by 2204z....or we don't.
Certainly frustrating as a passenger, but you've got to respect the intent behind the limitation and be thankful you don't have pilots who are put in a situation of landing in a snowstorm after 5 legs and a 17 hour duty day.
DRW