Economic troubles in Europe and Asia also may be taking a toll on American factories. Manufacturing employment dropped by 16,000 in September after falling by 22,000 in August.
Factory hiring had been a source of economic strength the past two years: Factory jobs rose last year at the fastest pace since 1997.
But Europe's ongoing economic crisis, along with a slowdown in China, means demand for U.S-made goods is drying up and "the days of robust manufacturing payrolls growth are likely behind us," said Chris Jones, an economist at TD Economics.
The unemployment rate has fallen from a peak of 10 percent in October 2009. But a big part of the drop over the past three years came because so many Americans stopped looking for work, so they weren't counted as unemployed.
Some were retiring baby boomers. Others were so discouraged by the weak job market that they stopped putting out resumes.
Economists were pleased with September's drop in unemployment because it happened for the right reasons: More Americans got jobs. And the work force grew by 418,000, the most since February, suggesting people are more optimistic about finding jobs. Because 873,000 more people did find work, the number of unemployed fell by 456,000. And that decline pushed the unemployment rate down.
Arthur Nazh was not surprised to hear that the unemployment rate fell. Business has improved this year at the kiosk where he sells souvenirs at a mall in Arlington, Va.
The economy "is getting better," said Nazh, 27, who employs six people and said he plans to vote for Obama because the economy needs more time to heal. "People are starting to buy more, spend more money."
Obama and Romney campaigned Friday in Nazh's home state and others that could tip to either candidate and determine the outcome of the election. Romney released three ads, mostly focused on jobs.
"These are tough times in this community," Romney, the former Massachusetts governor, told a rally outside a construction equipment store in Abingdon, Va. "We're going to bring back jobs and bring back America."
At a campaign stop in Cleveland, Obama declared: "We are moving forward again."
"Today's news should give us some encouragement," the president told thousands at Cleveland State University. "It shouldn't be an excuse for the other side to try to talk down the economy just to try to score a few political points."
The political back-and-forth over the unemployment numbers underscored the centrality of jobs to the election after a year in which the economy has been difficult to read.
The job market got off to a strong start in 2012. Employers added an average 226,000 jobs the first three months of the year.
Hiring in January, February and March was probably even stronger than that: The Labor Department has said 386,000 more jobs were created in the year that ended in March, but it has not assigned the jobs to specific months yet.
Job growth slowed sharply to an average 67,000 a month from April through June. And the weakness appeared to have continued into the summer, raising fears that a slow and steady economic recovery was losing momentum.
But the revisions to the July and August figures on Friday eased those fears somehwat. Monthly job growth was back up to an average 146,000 from July through September.
Naroff, the economist, predicted that unemployment would inch back up, and that job growth would settle at about 150,000 per month for the next several months. Economists at PNC Financial Services Group predict job growth will accelerate to 170,000 per month in 2013.
The economy is still far from full health. The number of U.S. jobs peaked in January 2008, a month after the Great Recession officially started, at 138 million. The job market shed 8.8 million jobs by February 2010. Since then, the economy has regained 4.6 million, or a little more than half, of those lost jobs.
No incumbent president since Gerald Ford in 1976 has faced re-election when the unemployment rate was as high as September's 7.8 percent, even after the sharp drop from August. Ford lost to Jimmy Carter.
Ronald Reagan faced 7.2 percent unemployment in 1984 and trounced Walter Mondale to win a second term.
AP Economics Writer Michael Sandler contributed to this report.