Two reports issued Thursday shed new light on trends in job-based health insurance before the launch of Obamacare, and what happened to the ranks of the uninsured after that health-care reform law kicked into high gear.
The first report, by the Robert Wood Johnson Foundation, suggests the recession accelerated an ongoing trend of declines in the percentage of private-sector American workers who get health insurance through their employer.
The second study, by the Kaiser Family Foundation, found that there were 11 million newly insured adults who had received coverage as a result of Obamacare by last month.
Read MoreThey want their Obamacaresubsidies
But that report also noted that almost half of the remaining 30 million people without insurance were eligible for either Medicaid or tax credits to buy Obamacare plans, but still failed to get covered, for a number of reasons.
Kaiser's study underscores the difficulty Obamacare advocates have predicted they will face in getting remaining uninsured Americans to buy into the program.
The Robert Wood Johnson report found that private sector workers with job-based coverage dropped from 53.7 percent in 2009 to 49.7 percent in 2013, the year that government-run Obamacare private insurance exchanges launched.
Worker participation in employer-based insurance "has been declining for more than a decade," according to Katherine Hempstead, who directs health coverage issues at the Robert Wood Foundation.
But the report largely blames the deep recession that began in 2008 for speeding up in the decline of covered workers.
Before the recession, the decreases in coverage of workers came from workers electing not to buy insurance, but afterward the decreases came more from workers having fewer offers of coverage, the report found.
Read MoreObamacare sign-ups hit 9.5M
The study noted that before 2009, the share of companies that offered workers health insurance nationally was "fairly stable," with 55.7 percent doing so as of that year. But that rate dropped to 50 percent of U.S. companies by 2013.
Thirty-five states "saw significant declines in the share of employers offering insurance to employees following the recession," the foundation said.
New Jersey saw the biggest decrease, with a 10.5 percentage point drop to 55.9 percent of employers offering health coverage.
"Most of the overall decline in the share of firms offering [employer-sponsored insurance] in the post-recession period was driven by small firms," the report said.
"The decrease in the post-recession period was nearly 12 times larger among small employers than large employers," according to the report, which noted the share dropped from "42.1 to 35.0 percent for small employers, and from 96.4 to 95.8 percent for large employers."
Hempstead said that, given the report's findings, "it will be interesting to see how that trend [of decline ESI participation] evolves now that there are more opportunities for coverage through the individual market and Medicaid."
Hempstead was referring to two main pillars of the Affordable Care Act.
The first was the creation of government-run insurance marketplaces to sell individual health plans. Tax credits, or subsidies, are available to low and middle-income customers of those plans, which can often significantly reduce the actual premiums they pay personally.
The second components was expanding joint federal-state Medicaid programs to expand eligibility of those programs to include nearly all poor adults, most of whom will pay no or little out-of-pocket costs for their coverage. Almost 30 states have adopted Medicaid expansion so far.
Both Medicaid expansion and the Obamacare exchanges have been credited with significantly reducing the rate of Americans without health insurance in 2014.
The Kaiser Family Foundation report released Thursday found that while those features had led to 11 million adults getting insurance in 2014 after lacking it, other factors were keeping the remaining 30 million or so adults from obtaining insurance.
Kaiser's report said that "48 percent of the roughly 30 million adults remaining uninsured at the end of 2014 were eligible for assistance under the law."
That included "30 percent who were eligible for marketplace tax credits, and 18 percent who were eligible for Medicaid," the report said. "And yet they did not get coverage."
The study found several key reasons for that.
A total of 53 percent of the uninsured eligible for help cited the perceived cost of health insurance generally as the primary reason they didn't have coverage.
And while some of those people who were eligible had in fact sought coverage, 37 percent of that group "say they were told they ineligible," the report found.
"While it is possible that they were ineligible at the time they applied, it is likely that these people received incorrect information or misinterpreted information they were given," according to Kaiser.
Rachel Garfield, a senior researcher at Kaiser, said, "The findings show how important it is to come up with more effective strategies, in person, online and elsewhere, for educating people about the eligibility for coverage and financial assistance under the law."
Kaiser noted nearly 4 million of the remaining uninsured are in a so-called "coverage gap." That means they live in non-Medicaid expanding states and earn too much to be on the Medicaid programs there, but also earn less than the income threshold for qualifying for Obamacare subsidies to buy coverage on government exchanges. Other uninsured people are undocumented immigrants, who are not eligible for Obamacare.
"No matter how well the ACA works, there are still substantial numbers of uninsured people with no affordable option for health coverage," said Kaiser Executive Vice President Diane Rowland.