Still, the economy and the job market remain lackluster. Even a gain of 125,000 jobs is only enough, over time, to keep up with population growth and prevent the unemployment rate from rising.

In April and May, employers added an average of just 73,000 jobs. That was far fewer than the 226,000 a month added in the first three months of the year. And it's far too low to reduce the unemployment rate.

Another weak month of hiring could benefit Mitt Romney, the presumptive GOP presidential nominee. President Barack Obama is expected to face voters with the highest unemployment rate of any president since the Great Depression, and the economy is the top issue for many voters.

Dismal June job figures could also prompt the Federal Reserve to take further action to try to boost the economy. The Fed last month downgraded its economic outlook for 2012. It predicted growth of just 1.9 percent to 2.4 percent for the year and little change in the unemployment rate.