I wouldn't pay the balance until it is due. Why give them all of your money for that long? I don't and have never had my price increase in the interim. Often the price has gone down, and it is easier to get the new lower price assigned to your booking when you still owe them money.
This is great advice! Always book early, and don't pay the final until due. If the general cruise fare goes up, you are protected, if it goes down, you can get adjustments up until the due date. You can still get adjustments even if you have paid, but as Dave noted, it is easier if you haven't.
The cruise lines don't pay interest on your money, so why tie it up with them? Or worse, pay interest on a credit card when it is not necessary.