I've read a few hundred m2 to a few hectares of land are needed per person to be self-sufficient. I guess it depends on what you are growing, your climate, and what you plan to do outside the growing season.

I have a friend with a couple of basic hoop greenhouses (around 8x2m) and for 6 weeks in summer they have more than enough tomatoes and cucumbers to provide for themselves to eat, to preserve and to give away to friends.

I think with a little planning, and only eating whatever is in season that week, you could easily grow enough in a 100m2 garden to provide all the vegetable needs for a family during summer. Planning is the important bit though, as some crops like broccoli need to be planted the year before. Oh and it's gonna be a hell of a lot tastier than what you get in the supermarket.