Hello Rissahh,
If you do not have a pssport, you will need two items: your original official birth certificate (OR a certified copy of your birth certificate) AND a government issued photo ID, (like your driver's license).
The only problem that you might encounter would be In the unfortunate event that you would need to cut your cruise short AND have to FLY back into the United States. Currently you must have a passport to FLY into the United States.
If you cruise next year you will need the passport then.