Without government job cuts, what's the unemployment rate?

If staffing levels were still at 2008 levels, the nation's jobless rate would be 7.1 percent instead of the current 8.1 percent, according to the Labor Department. Well, it might be a little higher than 7.1 percent because not as many people would have left the labor market (a higher labor pool often results in a higher unemployment rate). But it does point out the effect those losses have had. From Real Time Economics:

The Labor Department's establishment survey of employers -- the jobs count that it bases its payroll figures on -- shows that the government has been steadily shedding workers since the crisis struck, with 586,000 fewer jobs than in December 2008. Friday's employment report showed the cuts continued in April, with 15,000 government jobs lost. But the survey of households that the unemployment rate is based on suggests the government job cuts have been much, much worse. In April the household survey showed that that there were 442,000 fewer people working in government than in March. The household survey has a much smaller sample size than the establishment survey, and so is prone to volatility, but the magnitude of the drop is striking: It marks the largest decline on both an absolute and a percentage basis on record going back to 1948.