Millions of Americans remained stuck in part-time jobs in September, but there's little evidence to support claims that the federal health-care law is to blame.

Part-time employment rose during the recession and remains far above historical norms. Critics of the 2010 Affordable Care Act have suggested the trend could be due to its provision that requires many companies to offer health insurance to full-time employees beginning in 2015. That rule, critics argue, provides companies with an incentive to hire part-timers—and some...