As the U.S. Supreme Court deliberates on a case that may very well undermine a central plank of Obamacare, the vast majority of people who have gained health coverage under the controversial program are happy with it, a new survey finds. A total of 86 percent of people who are newly insured through private Obamacare health plans or Medicaid are very satisfied or somewhat satisfied with their coverage, according to the Commonwealth Fund report. (Tweet this) That report, issued last week, also reveals that almost 7 out of every 10 adults who are newly insured through either Obamacare private plans or Medicaid have actually used it to get health care. And more than 60 percent of those said they would have been unable to get or pay for that treatment without that new coverage, according to the survey.

They really, really like it

"The Affordable Care Act's coverage expansions have been in place for nearly 18 months, and indications are that the newly insured are pleased with their coverage and are using it to get needed health care," said Dr. David Blumenthal, president of the Commonwealth Fund. Yet the findings come as many of the newly insured are at risk of losing their health plans because of a pending Supreme Court case that could lead to federal financial aid for Obamacare insurance premiums being barred in 34 states. If the high court rules for plaintiffs in that case, 6.4 million HealthCare.gov customers would lose their Obamacare subsidies—and many are expected to drop their insurance altogether. Numerous other non-subsidized customers may also drop coverage after facing much-higher premiums that would occur in those states. Read More

Drop in uninsured

An agent from Sunshine Life and Health Advisors offers insight to potential enrollees in Miami about the plans available last year under the Affordable Care Act. Getty Images

The implementation of the ACA in recent years has led to a sharp decline in the number of Americans without health insurance, a fact touted by the Obama administration. The Commonwealth Fund survey found that, since 2013, the year before Obamacare marketplaces opened, the rate of adults without health insurance fell from 20 percent to 13 percent as of this year. The survey questioned 4,881 adults ages 19 to 64, and had a margin of error of +/-2.1 percentage points. The gains in coverage are split between uninsured people enrolling in plans sold on government-run exchanges, and enrolling in Medicaid, the federal-state health coverage system for the poor. The ACA allowed states to loosen their eligibility requirements for Medicaid to include nearly all poor adults. But 21 states have opted not to expand Medicaid. The survey found that nationally, the uninsured rate among low-income adults had fallen from 33 percent in 2013 to 26 percent as of May 2015. Read MoreStates lack 'plan B' for Obamacare aid

But the uninsured rates declined much more significantly in states that expanded Medicaid, from 28 percent of low-income adults in 2013 down to 16 percent in May. In the 22 states that had not expanded at the time of the survey, the uninsured rate of that income group barely budged during that same time frame, from 40 percent down to 38 percent.