Did Obama's union biased Stimulus slightly increase the number of workers in unionized firms?

All those rules requiring that work be done by unionized workers only had a small (I assume temporary) impact on the percent of workers who are unionized. From the WSJ:

The percentage of workers who belong to a union inched down to 11.8% from 11.9% in 2010, a decline the Bureau of Labor Statistics said left the rate "essentially unchanged." . . .

In 2011, the private sector added about 110,000 union members, pushing the total there to 7.2 million. In the public sector, membership fell by 61,000 as budget-strapped federal, state and local governments cut jobs.

Still, public-sector union members continued to account for more than half of the nation's total union members, and their membership rate of 37% remained five times greater than the private sector's rate of 6.9%. . . .