In fact, the decline in hiring — it was the worst month since last October — may not have been solely due to the storms that devastated Florida and Texas.

"Hurricanes Harvey and Irma hurt the job market in September," Mark Zandi, chief economist at Moody's, said in a statement. "Looking through the storms the job market remains sturdy and strong."

Private payrolls grew by 135,000 for the month, a sharp decline from the 228,000 in August, according to a report released Wednesday by ADP and Moody's Analytics. However, the number actually cleared the 125,000 that economists surveyed by Reuters had expected.

One of the worst hurricane seasons ever put a dent in September hiring, though it could have been worse.

A person walks through a flooded street in the Brickell area of downtown as Hurricane Irma passes through on September 10, 2017 in Miami, Florida.

The slowdown also may have come "due to a lack of competitive compensation to attract skilled talent," said Ahu Yildirmaz, vice president and co-head of the ADP Research Institute. The lack of strong wage growth has been attributed in part to employers struggling to find skilled workers, though Yildirmaz suggests that employers simply may not be offering higher pay.

Job growth was concentrated at larger firms, with businesses that employ 500 or more workers growing by 79,000. Smaller firms seemed to be hit the most by the storm damage, as companies that employ fewer than 50 workers saw their staffing decline by 7,000.

On the other side, goods-producing firms saw a sizable boost in hiring, gaining 48,000 positions thanks to a jump of 29,000 for construction as well as 18,000 new positions in manufacturing. Mining and natural resources also continued to grow, adding 1,000.

Not surprisingly, services accounted for the bulk of the job growth at 88,000 new jobs. That was led by a gain of 51,000 in professional and business services. However, the sector was held back by a decline of 18,000 in the usually strong trade, transportation and utilities sector and a drop of 11,000 in information services.

Education and health services added 29,000 while leisure and hospitality grew by 20,000.

The ADP/Moody's report comes ahead of Friday's key nonfarm payrolls report, with is expected to show a gain of just 93,000. That would be down from August's 156,000, which included a gain of 165,000 in private payrolls and a decline of 9,000 in government jobs. However, the ADP/Moody and Labor Department reports often differ significantly; August's disparity for private payrolls was 63,000 even after ADP and Moody's revised their count down by 9,000.