This happened to us a couple of years ago. A job change that we'd been hoping/praying for happened suddenly, but caused quite a hiccup in our savings (had to wait 4 weeks to get first pay on new job), so $$$ that we'd set aside to finish paying for our trip became necessary.
We book through a TA, so we contacted her AS SOON as we knew we'd need another week, and she contacted Disney for us. If you book directly, you'd just need to contact WDW directly. Anyway, we learned that reservations aren't cancelled until 30 days, which gives you a 14-15 day grace. Problem is, the payment MUST BE PROCESSED by 30 days, so you really need to get it in at least a couple of days before the 30 day mark.
We only needed another 7 days, thankfully, but I was sweating bullets that whole week

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Disney emailed us a copy of their cancellation policy, so we knew what we had to do and by when etc.
Your travel documents won't be released until your trip is paid in full, btw.
Hope that helps!