For opponents of the 2010 health care law, this has become one of the most popular talking points: The mandates on business will force Americans out of full-time jobs and into part-time work.

The claim rests on the law’s requirement that midsize and large employers offer health insurance to employees who work more than 30 hours a week or pay a fine. That argument has gotten a workout in recent weeks as Capitol Hill Republicans have refused to fund the government unless Democrats agree to broad changes to the law. It’s also found support among some labor unions, which worry their members will be pushed out of full-time jobs.

The problem with that argument is that it’s very hard to prove. The number and share of American workers who would like full-time jobs but who are stuck working part-time, which spiked during the recession, has actually been going down since 2010, when the law was passed. And although there has been some anecdotal evidence of employers shifting workers to part-time — stories that Republican lawmakers have latched onto — there’s no evidence that those stories represent a broader economic trend.

That hasn’t stopped labor officials and Republicans on Capitol Hill from predicting a dramatic affect on full-time work as a result of the law.

“Obamacare is hurting millions of people,” said Sen. Ted Cruz, R-Texas, in a Sunday CNN interview. “It’s killing their jobs. It’s forcing them into part-time work.”

Rep. Jim Bridenstine, R-Okla., pointed to companies in his district as an example during a news conference last month.

“Just recently I talked to a business,” he said. “They’ve got 57 employees. They’re trying to get down to 49. Other businesses are moving full-time workers to part-time workers.”

And in July the heads of three major labor unions wrote to House Minority Leader Nancy Pelosi of California and Senate Majority Leader Harry Reid of Nevada urging changes to the law, saying it would “destroy the foundation of the 40-hour workweek that is the backbone of the American middle class.”

Under the law, employers with 50 or more employees must offer health insurance to all workers employed for more than 30 hours a week or face a penalty of $2,000 per worker.

The “employer mandate” was supposed to go into effect on Jan. 1, 2014, but the Obama administration delayed implementation by one year, a move that Republicans have called a giveaway to big business.

While there may yet be a surge in involuntary part-time work once the mandate starts, evidence suggests the impact will be relatively limited.

A study earlier this year by the Labor Center at the University of California, Berkeley, estimated that roughly 1.8 percent of the U.S. workforce is at risk of being placed into part-time work as a result of the law. While that share is relatively modest, it still represents 2.3 million workers, according to the study.

The study looked at workers working 30 to 36 hours a week who did not have health insurance through their employers or through a family member. But because of data limitations, it only included employers with 100 or more employees, which means it may underestimate the true effect of the mandate.

That study follows a report last year by the Urban Institute looking at the effect of the 2006 Massachusetts health care law that served as a model for the 2010 legislation. In Massachusetts, the law “had little negative effect on private sector employment.”

While the report acknowledged some differences between the two laws, it said the results in Massachusetts “suggest that national health reform does not imply job loss and stymied economic growth.”

And another study published in the American Economic Journal: Economic Policy found that a requirement in Hawaii that employers offer health coverage to workers working 20 or more hours a week only increased the share of workers working fewer than 20 hours a week by 1.4 percent.

The Federal Reserve Bank of San Francisco concluded in August that “both the impact of the law so far and the ultimate effect are likely to be small.”

And despite the anecdotal evidence of employers shifting people to part-time work, it remains to be seen whether the trend will be widespread.

A recent survey by the Federal Reserve Bank of Minneapolis found that 89 percent of employers in the bank’s district said they would not shift people into part-time jobs.

“In terms of significant effects, we haven’t seen that yet, and these adjustments seem to be anecdotal and appear to be fairly minor,” said Mark Perry, a visiting scholar at the American Enterprise Institute and an economist at the University of Michigan-Flint. “That is kind of against the consensus that this is going to lead to part-time nation.”

To be sure, the number of people working part-time even though they want to work full-time has shot up over the past few years. But much of that increase is because of the lingering effects of the recession. It’s common for the number of part-time workers who would prefer full-time work to spike during downturns before dropping in recoveries. Businesses find they no longer need workers to work so many hours, for instance. Or job-seekers realize the only jobs that are available to them are jobs that are by nature part-time, such as bartending or retail jobs.

In this case, the sputtering recovery has kept the number of involuntary part-time workers elevated. The number of people working part-time who would rather work full-time doubled between September 2007 and May 2009. It has dropped since, but remains higher than at any point before the recession.

According to the San Francisco Fed, however, the share of all workers who work part-time is not historically high. At its most recent peak, in 2010, 19.7 percent of those employed worked part-time, slightly lower than the 1983 peak of 20.3 percent.

Unlike earlier recessions, however, there has not been a sharp drop in the share of part-time workers during the recovery. The Fed report says that “reflects a slow recovery of the jobs lost during the recession rather than permanent changes in the proportion of part-time jobs.”

Heidi Shierholz, a labor economist at the left-leaning Economic Policy Institute, said what’s happening with part-time workers is emblematic of the slow recovery.

Once businesses start seeing new demand for their goods and services they will start hiring workers again and converting some of their part-timers to full-time employees. That change will come as a result of economic fundamentals that will hold sway despite the insurance mandate.

“I don’t think part-time work is taking over,” she said. “When we do generate a robust job recovery, all of the data point to that we will return to the pre-recession share of part-time work as a share of overall employment.”