This story has been corrected to reflect the finding that under Obamacare, 4.2 million people may give up employer-provided insurance and choose a publicly subsidized plan instead. Of those, as many as 940,000 could quit their jobs. A previous version of the story said 4.2 million people could quit their jobs.

Pop quiz: Why do Americans have jobs?

If your answer is, to earn money, you’re only partially right. There’s one other important reason: To get health insurance. And as President Obama’s health-reform law starts to go into effect, it could give hundreds of thousands of workers a reason to quit.

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A new study distributed by the National Bureau of Economic Research finds that somewhere between 530,000 and 940,000 Americans might quit their jobs after January 1, 2014, as they’re able to get affordable health insurance through one of the public exchanges to be set up under Obamacare. That could provide ammunition for both critics and supporters of the politically explosive law. Critics might see it as evidence that Obama’s reforms encourage idleness while contributing to a growing welfare state. But it might also be a sign that workers have more freedom to pursue meaningful work or other interests instead of sticking to one job just because of the benefits, a phenomenon economists have dubbed “employment lock.”

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Study authors Craig Garthwaite, Tal Gross and Matthew J. Notowidigdo arrived at their estimate by studying changes in Tennessee’s Medicaid program, which expanded in 1994 to include more people, in ways similar to the way Obamacare will be structured. Costs became unaffordable, however, and a decade later the state forced about 170,000 childless adults—roughly 4 percent of the state’s working-age population—out of the program.

Related: Just Explain It: Five Things You Might Not Know About the Affordable Care Act

The researchers focused on what those people did for insurance once they could no longer get it through the state. For starters, there was a sudden surge in Google searches emanating from Tennessee and including phrases such as “job openings,” while there was no such surge in neighboring states. In the two years following the change, employment levels among childless adults in Tennessee—the same group knocked out of Medicaid—rose by 5.7 percent, a far bigger jump than elsewhere. And sure enough, by 2006 there was a sharp increase in the percentage of Tennessee adults with private insurance. Losing subsidized public insurance, in other words, forced more people to get jobs.

The opposite may happen with Obamacare, since under the program, anybody under 65 should be able to get insurance at a public exchange, with no income requirement except that those who earn more will pay a bit more for coverage. (Those 65 and over will already be covered through Medicare.) There are about 8.9 million Americans who earn too much to qualify for Medicaid and who also get health insurance through an employer. The study estimates that, based on what happened in Tennessee, 4.2 million of those people will switch from employer-provided insurance to a publicly subsidized plan under Obamacare. Of those, as many as 940,000 could quit their jobs, since they work primarily for the insurance coverage and enroll in Obamacare instead. That’s far higher than other estimates.

On the surface, that suggests Obamacare will create an incentive not to work while shrinking the size of the labor force. But that‘s not the same thing as killing jobs, one of the charges frequently levied against Obamacare by Republican critics of the law. The study authors point out that people entering or leaving the work force by choice, because of the need for insurance, is different from employers reducing payrolls because of insurance or labor costs. Some of the people who leave jobs and opt for Obamacare could be workers close to retirement age who aren’t yet eligible for Medicare, or spouses who took a job with benefits simply to obtain insurance coverage their working spouse can't get. Besides, with unemployment high, there’s an oversupply of workers in many industries, so for every person who leaves the labor force, that might mean somebody else gets a job.