The most economical option is to camp at Ft. Wilderness, but it takes a special kind of family to be able to do that. I know we couldn't!
Depending on the age of your children you may be able to stay in a value resort. They accommodate 5 if the youngest child is under 3 years old. Something I'd consider is staying at the Ft. Wilderness campground in a cabin. These work for 6 people and include a full kitchen so you could prepare many (if not all) of your meals in your room for far less money. Or you could also rent a condo or small house off-property and that kitchen. You can bring a small cooler into the parks with your lunch and snacks in it, so you wouldn't have to travel back for meals.
Some other money-saving tips...buy souvenirs in advance. Look for sales in the Disney Store or on
www.disneyshopping.com and get tees and toys that way, and surprise your kids when you get to a park. I go to the dollar store and buy rain ponchos and glow sticks, and you could pick up an autograph book there also for a great inexpensive souvenir. When you eat in the parks consider sharing meals (they are quite large), and remember that counter-service restaurants will give you ice water for free. I'd also suggest forgoing the park hopper option and just getting base tickets. Park hopping is not a necessity for a great trip and it will save you a fair amount to skip it. I'd also strongly caution against buying tickets somewhere other than Disney. Tickets are not transferrable, and I've heard many horror stories about someone who bought tickets at a deep discount only to find out that they were worthless. A mistake like that can really ruin a vacation, so be very cautious about where you buy.
If you have any other affordability questions we'd love to help you plan. It really IS possible on any budget, so don't be intimidated. Where there's a will there's a way!