US Customs and Border only require a birth certificate and government issued id for US citizens re-entering the US on closed-loop cruises. A closed-loop cruise is defined as a cruise leaving and returning from the same port in the US. This is the vast majority of cruises from the US.

Also many western hemisphere countries including almost all of those in the Carribean have agreements in place which allow US citizens arriving and departing via a cruise ship to need only a birth certificate and government id.

Traveling with a passport is best practice, you for instance are in trouble if miss your ship for some reason, but is not required for the vast majority of cruises from the US.