I had an experience like this several years ago, traveling on US Air; actually my first trip to Disney in 2000. There was a huge accident in my area that took the power out for the entire west side of town, about fifteen minutes before my alarm was to go off at 2:45 am. I woke up at 3:05 am....
I called the Airlines main number, as instructed by my TA (I used one at the time) immediately, gave them my name and confirmation number and told them what happened. She told me to proceed to the airport as quickly as I could possibly get there, but safely and not to worry.
When I got to the airport, I used the skycap and told them what happened. He immediately took me to the front of the line and inquired if the flight had been delayed. Sadly, it left on time and I literally missed it by five minutes.
They booked me on a later flight, that did not leave for almost 2-1/2 hours, so be prepared to wait. Also, I was third in line on stand-by, and that flight was booked solid, so I was only going to get on if three people didn't show up.
Two people didn't show up and the two people ahead of me got on, and we waited another two minutes for last call - and someone did not show up and I gladly got on - the next flight was not for another three hours.......
I got down the gangway and around the corner just as the guy was literally hurling my luggage into the baggage hold below and slamming the door shut - I didn't think it was going to survive the trip - but it did. And my luggage was the first one out the baggage claim and it had a couple of extra tags on it, just in case I got bumped again.
Believe me, it isn't fun.... but I made it there in one piece so I was grateful.