Agweb has an interesting discussion of the size of farms. The argument is that one person can manage up to 10 employees, which is about enough to handle 10,000 acres. (I'm assuming we're talking grain or cotton crops here as I imagine produce or livestock would have a different scale.) Any more and you're talking a real organization, where the top person is managing managers.
I guess one could grant the title "family farm" to such farms--after all back in the 1870 census my great grandfather had a hired hand living in household and he only had 300+ acres. But that's stretching it--I'm too lazy today to see what ERS says about farms where most of the labor is hired.