The percentage of companies offering health insurance to their workers and families and the percentage of acceptance of such offers both have remained steady since implementation of the Affordable Care Act, according to the Health Reform Monitoring Survey , funded by the Urban Institute and Robert Wood Johnson Foundation.

Obamacare still hasn't led to drops in the numbers of people who get health coverage through their jobs, despite some earlier fears that would happen, according to a new survey released Wednesday.

Finally, the report found that offers of job-based health coverage actually increased among workers who have the lowest level of education, and that job-provided coverage rates likewise increased among Hispanic workers.

Those people include workers with low education, racial and ethnic minorities, those who live in areas with stronger options for government-sponsored health care and employees of small businesses.

The survey — which looked at the period between June 2013 and March of this year — also found that insured rates among people with employer-sponsored coverage "remained stable among workers most susceptible to declines" if such coverage "were to erode under the ACA."

"Concerns about employer-sponsored health insurance evaporating after the implementation of health reform have not materialized," said Kathy Hempstead, who directs the Robert Wood Johnson Foundation's work on health insurance coverage.

"Time will tell if the Affordable Care Act leads to fewer people with insurance through their jobs, but as of now, the law has had little to no effect on employer-sponsored insurance," Hempstead said.

Employer-sponsored insurance is, by far, the the most common source of health coverage in the United States.

There are an estimated 155 million people under age 65 covered by such plans. That dwarfs the 76 million or so people covered by Medicaid, the government-run program that benefits primarily poor people and children, and the approximately 55 million covered by Medicare, the government program primarily for senior citizens.

Just 11.1 million people are currently covered by Obamacare plans sold via government-run marketplaces.

The ACA began taking full effect in 2014. That year was the first in which most Americans were required to have some form of health coverage or face a tax penalty. It was also the first year of coverage from private health plans for individuals and their families that are sold on Obamacare exchanges, often at heavily subsidized prices.

At the same time, enrollment in Medicaid began ramping up significantly as growing numbers of poor adults became eligible for that program due to ACA provisions that encouraged states to loosen their sign-up restrictions.

The Urban Institute report noted that in the 12-year period before 2013, there was a marked drop in the rate of people covered by job-based coverage. "Some have argued that the changes introduced by the ACA would accelerate this trend because the greater availability of coverage outside of work would make it easier for employers to stop offering coverage," the report said.

But that didn't happen.

The report found that in June 2013, 70.8 percent of all workers between the ages of 18 and 64 had employer-sponsored insurance coverage. As of last March, nearly three years later, 72.1 percent of all such workers have job-based coverage. Similar, incremental upticks were seen in the rates of job-based coverage among the two major subgroups of workers: people at small firms, and people at large firms.

In June 2013, the share of nonelderly adult workers who were offered job-based coverage stood at 82.4 percent, according to the report. Nearly three years later, with Obamacare in full swing, the offer rate was 83.1 percent.

Again, there were slight increases in the offer rates for people in both small firms and large firms, and there likewise were little if any differences seen in offer rates when people in different income groups were looked at, the report said.