My stepdad says that 2000 is too much money. Help.
If you don't have to fly to get there, that will be your first savings.
You can stay at a hotel off of Disney property, that will save you a lot of money.
Your next biggest expense will be park tickets, which is hard to save anything on.
Then food. Eat outside the parks as much as possible, or eat as little as possible.
It can be done, just do some research.
Two discounted 4 day tickets will be $603. Parking would be $80 (unless you are staying at a value restaurant)- plus food?
Given the math from @PrincipalTinker, that leaves you $320 for a room. I don't think you could find a ghetto roach motel for $50/night in Orlando. And if you could, that would leave you $20 for the two of you to eat for the week...
Even when I have an AP and stay at a value with a really good military discount. I'm hard pressed to do a week, solo, for less than $1000 - and that's without any signature dining. Then I have to add $150-200 for gas to get me there and back...
You are almost $700 with parking and tickets. 4-5 nights of a hotel would be extremely hard to find for $300. Then food and whatever transportation you use to get there. $1500 may be doable if you can drive down in under a day and stick to groceries for almost all meals. I wouldn't really consider groceries an expense since you have to buy them at home anyway. Good luck!
Edit: You could stay in a campground and tent for $50/night if you had the gear. That may be the cheapest option. Easier to cook than a standard hotel room.
Keep an eye out for the deals Disney throws out from time to time. "Play, Stay, and Dine" can get you hotel, 4 day tickets, and discounted dining plans. I got it in February 2015.
The 4-day ticket special they're running right now would help a little. 2 adult tickets would be $594, including taxes, and you can go to each of the parks for one day. That leaves one day off to relax outside WDW, which will save a little money.
You can camp at fort wilderness on property for I think $50 per night.