In previous years, not much of a chance. But this year, it's possible. If you're set up with a disneyland.com account and you've added your AP number to it, you can see that they have up to 40% off at the disney hotels through April 30th... That's unusual. So they might continue to extend the good deals.
Luckily you can book something then call later if you see a deal, and put that deal onto what you have. In case you don't know, you will pay a one night deposit when you book, and the rest will be due at checkout.