I wouldn't stress about it too much. Yes, we here on Cruise Chat are big proponents of flying in the day before. It is just a huge stress reliever. But, what is done is done. In reality I think a huge majority of the cruisers come in the day of the cruise (all the cruise line arranged air travel comes in on embarkation day) so more often than not everything goes fine. We just have the experience to know that things don't ALWAYS go as planned with air travel and suggest you don't try the same day flights.
Do as Cruise Fanatic suggests and see if you can find travel insurance that will cover your trip. That way if the worst happens and you miss the ship, the insurance will cover your cost to get you to the next port to meet the ship. Also be sure to have the cruise line's contact phone number with you so if the plane is delayed you can contact the cruise line. Knowing where you are and that you are on your way can go a long way and possibly allow you to make the ship if you are a last minute arrival.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013