Most states only allow you to have one ID, either a driver's license or a regular ID. If one lives in a state that allows two then it's an option for sure. If someone works for a government entity then their employee ID would work as long as it has a picture on it.
OP, crossing my fingers that your new license does come in before the cruise. If your means of getting to the port have been paid for or cost little then if it were me I'd probably show up with what I have since the only people that can tell you for sure if that would work are in the terminal itself. If boarding is denied you are in no worse shape than you are now and best case is you still get to cruise so you can relax from all this tension. As mentioned any pre-paid items other than the fare would still be refunded.