Sorry to hear about your financial issues.
First suggestion would be to call your carnival rep and see what can be done. For our 5 day cruise, if we had chosen not to pay in full, we had to have it paid of 60 days from our cruise date.
Second suggestion would be to start pinchin' your pennies and make small payments a bit at time if necessary so you don't have as much to pay off. You'd be surprised how much that can add up and ease the burden. =P
Third - although I wouldn't normally tell people to automatically go the credit card route - yes, Carnival does offer one AND, it has no interest for 12 months so that might be an option and buy you a little time to finish it off. Then, if necessary you could always use it for your "spending" on the ship too and then you'd be covered for any unexpected charges that Don was talking about. I personally have never had those unexpected expenses but that doesn't mean that it doesn't happen to some. Just make sure you pay it off in the 12 months and you'll not have to worry about the interest. (plus you can get some points to use for OBC and such if you have enough) It could just save your butt in this situation.
Hope it all works out for you and you get to go. There are lots of tips to save money on the ship through the forums. If you get it all worked out, just relax, have fun and don't stress about it all. Good luck!