<must...not...plug...Fantasy...walkthrough...video>
Getting a passport is just a good idea. While you won't need it to board the ship, it is considered true "international" identification and proof of citizenship.
Two reasons why it's important if you are leaving US soil.
1) If you needed to be transported due to (forbid) a medical or other unforseen emergency, without a passport, you will not be able to travel.
2) If something happened (again, forbid) while you were at a port of call (really...ANYTHING...could happen from domestic unrest to criminal acts...unlikely, HIGHLY unlikely...but possible)... The US Passport is the only official documentation that is internationally recognized as proof that you are a US Citizen, and if you ever had...for whatever reason...need to utilize the services of our Diplomatic Corps (Department of State) you will need to have that proof.
So, in short, go ahead and get it. It doesn't take very long, and isn't that expensive...and it last 7 years. So, to me, better safe than sorry!