I couldn't find a source (beyond tons of articles echoing the study), and found several contrarian sources, including http://www.wiredacademic.com/2012/01/unemployment-data-most-...
The Bureau of Labor Statistics is always a great place to look.
Employment status of the civilian population 25 years and over by educational attainment: http://www.bls.gov/news.release/empsit.t04.htm
According to this (last updated Dec 02, 2011) the not-seasonally adjusted aggregate unemployment for anyone who holds a HS diploma (regardless of higher level education) is 20%.
Edit: I didn't mean to cause any confusion by aggregating the "non-hs-dropout" stats, so let me make it clearer:
Level of Education : Unemployment Rate High School Dropout: 12.7% High School Diploma: 8.4% Some College/AA Deg: 7.4% Bachelors or Higher: 4.2%
That is exactly what I did. In my original response, I wrote aggregate unemployment for anyone who holds a HS diploma (regardless of higher level education) is 20%. I wasn't trying to be misleading, I just thought it was interesting to see that the aggregate for all non-high school dropouts.
Anyway, after looking at the article again, the author claims the unemployment stats come from 2009-2010 US Census and a study done at the Georgetown Center on Education and Workforce, broken down by age group. The BLS scope is obviously much larger and current.
The aggregate unemployment rate for those groups together is 7.4%, not 20%.