While that is indeed a gain of 4.5 million, it's only a net gain of 300,000 over the course of the Obama administration to date. The private jobs figure stood at 111 million in January 2009, the month Obama took office.
And total nonfarm payrolls, including government workers, are down from 133.6 million workers at the beginning of 2009 to 133.2 million in July 2012. There's been a net loss of nearly 1 million public-sector jobs since Obama took office, despite a surge in temporary hiring for the 2010 census.
Source: CNN. Read full article. (link)