Many who oppose the requirement say the cost of providing health insurance could mean hiring fewer workers. “Any dollar that gets diverted, whether it’s through Obamacare or increased tax rates, puts franchisees one dollar further away from being able to expand their businesses,” said Don Fox, chief executive of Firehouse Subs, a fast-growing chain of 559 restaurants based in Jacksonville, Fla. At the 30 stores the corporation owns, only full-time managers are offered coverage. Mr. Fox is wrestling with whether to absorb the considerable cost of covering 100 more employees or pay the penalties — which would probably cost him less — but risk losing valued employees to competitors who choose to offer coverage.

Employee health coverage now averages nearly $6,000 for an individual plan. That is considerable for businesses like restaurants in which the majority of workers make $24,000 a year or less, according to research by the Kaiser Family Foundation. The foundation found that only 28 percent of companies that employ large numbers of low-income workers offer health benefits. “This is where the biggest set of hurdles is,” said Gary Claxton, an executive with Kaiser.

By 2014, businesses with 50 or more full-time employees will be expected to offer as yet undefined affordable coverage, based on an employee’s income. For employers that fail to offer such coverage, the law typically calls for a penalty of $2,000 a worker, excluding the first 30 employees. As evidence of how sensitive the issue is, Mr. Schnatter of Papa John’s took some heat for his initial statements about the possibility that franchisees would cut employees’ hours to avoid penalties or having to provide coverage. His comments, made during a public appearance, were reported by a local newspaper in Florida, The Naples News. After facing a storm of criticism, he wrote an opinion piece for The Huffington Post, in which he said he had only been speculating about the law’s potential impact on franchisees.

“Papa John’s, like most businesses, is still researching what the Affordable Care Act means to our operations,” he wrote. “Regardless of the conclusion of our analysis, we will honor this law, as we do all laws, and continue to offer 100 percent of Papa John’s corporate employees and workers in company-owned stores health insurance as we have since the company was founded in 1984.” Through a spokesman, Mr. Schnatter declined to comment further.

Some business owners and consultants warn that opting to have more part-time workers, perhaps by converting some full-timers to part-time status, may not be the answer because many workers might decide to find jobs elsewhere.

“When you explain this to your employee who really needs the income, maybe they’ll try to get a second job,” said Mr. Fox, Firehouse’s chief executive. “Maybe they’ll try to get another full-time job and maybe a job that provides health care. There will be an incentive for the best people to search for those jobs.”