ATLANTA—A sharp uptick in jobless numbers across a slew of Southern states has baffled economists and rattled at least one big political race.

It has also raised an unusual question: Is the trend real?

When the Labor Department last month said Georgia’s unemployment rate had jumped to 8.1% in August, making it the worst state for joblessness in the country, Democratic gubernatorial challenger Jason Carter seized on the news.

Gov. Nathan Deal, he said, “has had four years to move Georgia forward, but he has only brought us to the bottom.”

Mr. Deal, in turn, suggested the data may have been manipulated for political purposes.