The expedited fee is hefty, and many passports have been arriving back in as little as 3-4 weeks this year. As long as you have a birth certificate (original or certified copy with raised seal, not just a xerox) and valid govt-issued photo ID (driver's license) you should be fine. However, passports may be required in the future, and we usually recommend our clients get them. If you can easily get several certified copies of your birth certificate, I would suggest going ahead & applying for a passport (first-timers I believe need to show up at the P.O.in person, not do it on the 'net) but planning to use your other ID for your December cruise, just in case.
Incidentally, if you have changed your name since birth, by marriage or otherwise, you will also need certified copy of that document as well (marriage certificate, name-change certificate, whatever.) You will probably also need that for passport application, as well as for ID on cruises.
Also, if you have any minors traveling along with you who do not have both parents along, they will need a notarized statement from the stay-at-home parent giving you permission to take the child out of the country. This is especially true in Mexico.