I was flying home from Mexico via the US with Continental and managed to wake up with horrible food poisoning, I was white as a sheet by the time we got to the airport. Continental were great and happy to put me on the next day's flight, but I wanted to get home so got on the plane anyway. It was the worst 15hrs traveling of my life but the crew were fantastic.

I think this was just an exception (perhaps they had plenty of spare seats) but it was nice to see and I know how you feel. However ultimately this is what travel insurance is designed to cover (though probably not worth it for short/cheap trips such as yours) rather than relying on the airline.