A tiny part of the nation’s unemployment problem starts high in the trees of Miami Shores.

That’s where Cairo Bonilla spent Friday morning on a cherry-picker truck, cutting down branches of a mahogany tree trying to embrace some utility lines. Bonilla, 44, used to be one of four tree trimmers on the city’s payroll. Now he’s one of two.

“It’s a very good job to have,’’ he said while helping the other half of his team, Alize Mere, load branches into a wood chipper. Miami Shores cut back to one tree-trimming crew after property taxes plunged during the real estate crash — one eddy in a wave of municipal cutbacks that continues to hold back the private sector’s rebound

On Friday, the Labor Department reported the nation’s employers added 96,000 jobs in August, a letdown since analysts expected 125,000. Stocks still managed to end the day up slightly, thanks in part to speculation that the weak jobs report will prompt the Federal Reserve to pump more money into the financial system as a way to spur growth.

At first glance, the national 8.1 percent unemployment rate for August looked encouraging, since it dropped from 8.3 percent in July. But the numbers behind the decline looked grim: about 370,000 people dropped out of the labor force altogether, which lowered the unemployment rate despite the number of employed people dropping by 119,000 last month.

In all, the report served up a statistical reminder that the economy remains weak, and the recovery spotty despite some encouraging signs of hiring in July.

“July’s jobs report hinted at an acceleration in the labor market after a weak second quarter. The August report has dashed those hopes,” IHS Global Insight chief economist Nigel Gault wrote in a note to clients Friday morning. “Jobs growth was anemic, and even the drop in the unemployment rate was bad news because it happened for the ‘wrong’ reason...”

South Florida will gets its August job report in two weeks. July’s unemployment rate was 7.6 percent in Broward and 9.5 percent in Miami-Dade.

The national employment numbers would have been a bit better if not for August’s continued dip in government hiring. Private employers added 103,000 jobs, while public employers lost 7,000 jobs. That’s part of a long-running trend in the recovery. Private employers have added jobs for the last 22 months, but government employers have added jobs only twice in the same stretch.

“It’s a difficult time,’’ said Kevin Kelleher, human resources director for Broward County, which he said has eliminated about 1,800 positions in the last five years. “Things will get better. But I haven’t seen the trends yet.”

Government payrolls make up a small portion of the overall economy — about 16 percent nationally, and 14 percent in South Florida. But government layoffs and hiring freezes have played an outsized roll in holding back a hiring recovery that began two years ago.

In July, the last month with South Florida employment figures available, local government accounted for one out of every three jobs lost in Miami-Dade County — second only to construction’s 40-percent share. In Broward, the ratio wasn’t as bad but still significant: local government accounted for 12 percent of jobs lost in July.