How much you'll need will depend upon what you'll need to pay for when you're there.
How are you getting from the airport to the hotel? If you're renting a car, you'll need to pay tolls along the way. If you aren't staying onsite, you'll need to pay for parking ($8/day). Are you taking a shuttle bus? If you haven't paid for it yet, Mears will charge about $29/adult RT. Plus you should tip the driver.
How do plan to eat? Are you big eaters? Light eaters? Picky eaters? Do you prefer to have a sitdown meal 3 times a day or will you just grab counter service and go? Will you be buying any groceries to keep in the room? All these factors will influence how much money you'll need to bring.
Are you big souvenir shoppers? Some people can go to WDW and return with nothing more than a t-shirt or refrigerator magnet. Then there are others that view WDW as a giant Mickey Mall. If you want to avoid spending too much money, close your eyes after exiting the attractions. Every ride empties into a gift shop. Disney likes to make it very convenient for you and your money to part.
I can tell you that we (DH, myself, DD14 and DS12) can survive on $125 per day very nicely with a rental car, onsite hotel and one sitdown lunch per day. We always carry Brita water bottles instead of buying water in the parks and we don't souvenir shop very much.