Friday's revisions show that those payrolls increased by 18,000 in July and 45,000 in August, putting together the first three-month stretch of growth in public-sector employment since the Census Bureau hired temporary workers in March through May 2010, according to Gary Burtless, a senior fellow in economic studies at Brookings.
Between May 2010 and July, private payroll employment rose more than 3.9 million, while government jobs dropped by nearly 1.1 million, Burtless said.
Revised figures show the economy added 181,000 jobs in July and 142,000 in August, a total gain of 86,000.
First estimates indicated that the economy added 141,000 in July and 96,000 in August.
The economy added only 114,00 jobs — 104,000 in the private sector in September — and the unemployment rate dropped from 8.1 percent to 7.8 percent.
Private-sector job growth has remained steady for 31 straight months and has been dragged down by persistent losses across the government, especially in states facing budget pressures.
Still, Burtless cautioned about getting too excited over the monthly job numbers, which can be volatile.
"While the September employment report was more encouraging than the ones we have seen in recent months, the job market is still a long way from rosy good health."