They have to get final payment sooner rather than later, because so many people cancel at final payment (or don't make it), and Carnival has to have time to resell the cabin. The same reason Carnival requires prepayment for shore excursions and these days specialty restaurants.
You can CALL Carnival and ask for an extension, but they aren't going to give you 60 days - maybe 2 weeks.
Carnival could cancel immediately and keep any penalty. If you have a desirable assigned cabin, they could switch you to a guarantee and resell your former cabin. Really they can do anything they want - if you don't pay on time you have violated the contract.