Republicans, and some Democrats, worried that employers would look for ways to get around the mandate, either by giving their employees fewer than 30 hours, or by hiring fewer people.
And GOP lawmakers in Congress have tried more than once to increase the limit from 30 hours to 40 hours per week, with idea of making it more difficult for businesses to avoid the mandate.
So far, though, researchers say employers have not changed how they hire and schedule their workers in response to the law.
"The data, to date, basically say that that hasn't happened, at least on aggregate basis -- that there really hasn't been nearly the change that some people were expecting," said Chris Ryan, a vice president at the payroll-management firm ADP.
Analysts at ADP studied the payrolls of the firms' clients, about 75,000 U.S. firms and organizations. They expected that as businesses prepared for the mandate to take effect, they would adjust their employees' schedules, limiting them to no more than 30 hours a week. Yet ADP found no overall change in employees' weekly schedules between 2013 and last year.
According to ADP's analysis, shifts in scheduling were trivial in every sector of the economy, even in industries that rely heavily on part-time work, such as leisure and hospitality.
Ryan explained that qualified workers have more options as the economy improves, and they're getting pickier. As a result, the priority for employers is attracting the best possible workforce. Hiring and retaining good employees means giving them what they want -- often, health insurance and full-time work.
"There is much more competition for people," Ryan said. "That becomes far more important than the cost of health benefits."
ADP's findings were confirmed in another study by Aparna Mathur and Sita Nataraj Slavov of George Mason University and Michael Strain of the conservative American Enterprise Institute.
Their paper, published this month in the journal Applied Economics Letters, uses data from the federal Current Population Survey and finds no statistically significant change in the proportion of part-time workers in the sectors most likely to be affected by Obamacare, such as janitorial and restaurant work.
The study, like ADP's analysis, only uses data from before the mandate took effect, on the assumption that employers would begin adjusting their workers' schedules beforehand. Yet Strain said that firms might still reduce their employees' hours in the future once they discover the cost of providing health care.
"There's still a big open question about whether the Affordable Care Act and the employer mandate will increase part time work," said Strain, an opponent of Obamacare. "That question has not been settled. Our paper provides evidence that that shift hasn't happened yet."
Bowen Garrett, an economist at the Urban Institute, disagreed. "It's reasonable to think that if there was going to be a large effect, some of it would have happened in 2014," he said. That was when the main provisions of the law went into effect, and around 15 million people gained health insurance.
This week, Garrett and his colleague Robert Kaestner published their own analysis of the federal survey data, coming to largely the same conclusions as Strain and his collaborators.
They found that circumstances for workers last year were what you would predict based on overall economic conditions in 2013. In other words, the economy has recovered steadily, and if Obamacare has had an effect, it has been too small to measure.
The researchers at Urban also examined a separate aspect of the law, the expansion of Medicaid to more beneficiaries.
For many people, health insurance is one of the most important reasons to find and hold down a job. Obamacare's conservative opponents predicted that if Americans could receive insurance through Medicaid instead of through an employer, some of them would leave the workforce.
Yet the Urban analysis did not find significant differences between states that expanded Medicaid and those that did not.
"There's been a lot of talk about the ACA reducing the number of jobs, or killing some jobs, and we simply don't see the evidence of that in the data that we've been able to examine up to 2014," Garrett said.