It’s actually a misstatement of the conclusions of research by Betty Hart and Todd R. Risley and reported in "Meaningful Differences in the Everyday Experience of Young American Children"
http://www.amazon.com/Meaningful-Differences-Everyday-Experience-American/dp/1557661979/ref=pd_bbs_sr_1/105-4026262-0762063?ie=UTF8&s=books&qid=1188430854&sr=8-1
What Hart and Risley actually found that three-year-olds of "professional" mothers (their term) used more words in interactions with their children than mothers on welfare.
The sample was around forty parents, total.
The study didn't address the the size of the adult vocabulary of either group of parents.
It’s a shame that Lyon (who has identified “Meaningful Differences” as the source of this Factoid) isn’t more careful – she has a lot of interesting things to say about class in the US.
Very interesting post!