A lot depends on who the flight is booked with. If it's booked with the cruise line or an agent as a complete package then it is their job to get you to the ship or refund your costs.
If you have booked the flight yourself separately from the cruise then you could have a problem.
If the latter, it always gives peace of mind to fly the day before the cruise and stay one night in a hotel near the terminal. Our agent does this everytime we go to Miami, or even Barcelona.
Book the flights independently and you are delayed, it's your expensive problem. Book a flight/cruise package, it's the problem of the cruise line/agent. We usually book flights independently and aim to arrive at the departure area at least 24/72hrs before the ship sails depending upon where in the world we are sailing from.