You will get a variety of responses here, as some people feel very strongly about their position regarding passports.
Technically...it is a closed-loop cruise and therefore you are certainly allowed to travel using only a drivers license and CERTIFIED birth certificates. Make sure you have the "official" full birth certifcate forms, not a simple form from the hospital or photocopy; it may have a raised seal, hologram or something else that makes it "official."
Now, many people feel that a Passport is a important expense because you are traveling to foreign countires (or foreign waters even if you don't plan to disembark). If any kind of emergency arises which might require you to fly home immediately, you will not be able to do so (easily) without a full Passport book - no you would not be stuck forever in another country, but your departure would be delayed while dealing with the embassy to get an expediated Passport to allow you to fly home. In a medical emergency, this could seem like a long time. Therefore, many people feel a Passport is "worth" the expense as "insurance" that they could return home when/if the need were to arise.
Many others deem the likelihood of such an emergency to be very low and therefore they cruise without a Passport book. You will need to determine your family's tolerance risk and weigh the expense of Passports. Feel comfortable in your decision either way. My family has Passport cards because we live near a US border, but the cards have no value for flying, however we decided we were comfortable cruising with just the card (I don't recommend getting a Passport Card just to cruise).
Enjoy your cruise!
