Finally figured out some better search terms. Several different sources indicate that there are at least 10 million people working in government as contractors (not counting the several million more military and post office) contractors. Here's
one article (which does mention that while official employment has remained flat, contractors have exploded during the last 20 years.
Here's a 2006 Washington Post article (which is pointing out that Bush was hiding the peanut in claming smaller government while hiring more contractors) that estimates 2.5 additional contractor positions between 2002 and 2006.