You could NOT have six people in a regular value room. For fire regulations, occupancy in these rooms is limited to four people, plus one child under the age three in a crib. And even that is tight. Roll away beds are not available, and at only 260 square feet for the entire room, there wouldn't be space for it.
The cheapest on-site accommodations for a family of six would be two connecting rooms at one of the value resorts. A close second would be a Family Suite at the All Star Music Resort. You can read all about this
HERE. The cabins at Fort Wilderness would be slightly more expensive still. Prices can change, but a recent price for a cabin during the least expensive season was $255 per night. Compare this with $164 for two connecting value rooms, or $184 for the Family Suite. (Again, prices can change.)
While two rooms is the least expensive option from a pure room-cost standpoint, the Family Suite has a kitchenette and the cabins have a full kitchen. You could perhaps save a bit of money on dining if you used these facilities to cook a few meals yourself, making these rooms a better overall value.