Disney on a $3000 Budget
This is probably the lowest reasonable budget I'd consider for Disney World trips. In the examples below, notice that transportation and park ticket prices stay the same even when the number of days changes. If you're staying somewhere that's relatively inexpensive and not eating out all the time, you can often extend a trip from 4 to 7 days for very little money.
Example 1: 6 nights at a WDW Value Resort during least busy time
Transportation: road trip with a night in a hotel on the way there and back ($200 for gas + $200 hotels = $400)
Lodging: 6 nights onsite at Pop Century during Value Season ($111 x 6 = $666)
Park tickets: 6-day base park tickets purchased from a third party like AAA or a ticket wholesaler ($320/adult and $300/child = $1240 for all 4)
Food: get groceries for breakfasts and packed lunches, eat a few dinners out ($100 groceries + $300 restaurants = $400)
Souvenirs/spending money: that leaves almost $300 for spending money