I was a member of Enright Eco Village in Cincinnati for two years when I lived there. 45 families were sustained with excessive amounts of produce on less than 4 acres of land from early May until November. The farmer that organized our plantings used techniques to maximize seedling growth and vegetable harvest. We focused on raising vegetables and harvested fruit from CSA members who already had preexisting trees/canes/etc. My opinion is that if 45 families live well on less than 4 acres, your family can do well with your current amount of acreage - it's all determined by how you garden. Yes, you can grow more than enough food for you family on that amount of land.
Use intensive planting methods- if it's not growing or doing well, rip it out and plant something else.
Grow from seed- it's cheaper to begin and you can save your own seed, through open pollination, to grow veges suited for your geographic location
make friends with a cattleman, equine boarder, or zoo keeper with keys to the "black gold" bins - manure will replenish that which you taketh away
read Square Foot Gardening and The Resilient Gardner - these two books help you with planning and with thinking about outcomes.
Guinea pigs - research feed to meat ratio
Enright's web page