The chart above (click to enlarge) shows monthly employment levels for private-sector workers vs. government workers, based on data from the BLS household survey (private sector employment is calculated by subtracting government employment from total nonagricultural employment). From the peak high in late 2008, government payrolls have decreased by more than 1.2 million workers through May, while the number of private sector workers has increased by more than 2.5 million since the peak low in late 2009.
The fact that private sector jobs are continuing to increase while public sector jobs are declining could be considered a positive side-effect of the 2007-2009 recession, i.e. the recession-related 5.6% contraction of public sector employment. In May alone, there was a decrease of 417,000 government jobs, following losses of 132,000 in April, and 75,000 in March, totaling 549,000 for the last three months, and that's really the main source of labor market weakness - it's mostly in the public sector, not the private sector.
Based on the household measure of private sector employment, there was a 373,000 job increase in May, following a 11,000 decrease in April, and a 370,000 increase in March. In comparison, private payroll jobs increase by only 83,000 in May, following increases of 251,000 in April, and 219,000 in March.
Year-to-date, one million jobs have added in the private industries according to the household survey, slightly higher than the 908,000 jobs added according to private payroll data. Either way, the household survey and payroll data are showing monthly private job gains of around 200,000 so far this year, suggesting that the labor market, especially for private sector employment, might have some underlying strength that is not showing up in today's Employment Situation report (pdf).