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Buried in a Kaiser Family Foundation survey in June was the finding that just 49 percent of people who signed up for insurance via HealthCare.gov said they are getting subsidies to help pay for their premiums. That's despite the fact that the percentage of HealthCare.gov enrollees who actually get those subsidies is actually much higher: 86 percent of enrollees are not paying their insurance plan's full sticker price because the federal government is footing some or much of the bill. Levitt said that even people who know they are getting subsidies for HealthCare.gov plans are unlikely to know that a Supreme Court decision in the Halbig case could render that assistance illegal. Such a decision would affect only subsidies issued through a federal insurance marketplace—such as HealthCare.gov—not the subsidies issued through one of 15 Obamacare exchanges run by an individual state or the District of Columbia. About 4.7 million people receive subsidies for their HealthCare.gov plans, which are sold in 36 states.

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A recent Avalere Health analysis said that for those people, their monthly insurance premium prices would rise an average of 76 percent if the subsidies were taken away.

In a controversial ruling last Tuesday, a federal appeals court panel in Washington, D.C., said that the Affordable Care Act, as explicitly written, only authorizes subsidies to be issued through state-run exchanges. The Obama administration and another federal appeals circuit's panel disagrees with that decision, saying the ACA allows subsidies for HealthCare.gov enrollees. For now, those subsidies remain in effect. But if the administration doesn't persuade the full D.C. appeals circuit to reverse its panel's ruling, the case would go to the Supreme Court, which could invalidate the HealthCare.gov subsidies. "This is a major, major threat to the ACA. If Halbig prevails, millions of people will lose access to subsidies," Levitt said. Still, he said, "I can't imagine that the average person grasps what's going on with this Halbig case." Read MoreObamacare could be saved by 'nuclear option'

Levitt noted that while Obamacare enrollees "are generally happy with their plans," as detailed in the June survey by Kaiser, "there are still concerns about their affordability." "Those [concerns] would be even more severe if their subsidies got taken away," he said.

Currently, people whose income is between 100 percent to 400 percent of the federal poverty level are entitled to taxpayer-funded subsidies from the federal government to help pay for monthly premiums of plans sold on a health insurance exchange run by either a state or the federal government. For an individuals, that is between about $11,670 to $46,680 annually, and for a family of four, it's between about $23,850 to $95,400 per year. A total of 86 percent of the 5.45 million people who signed up for insurance sold on HealthCare.gov qualified for a premium subsidy. Those subsides are, on average, very generous. According to the U.S. Health and Human Services, nearly 70 percent of people receiving Obamacare subsidies are paying $100 or less per month in premiums for their insurance, while 46 percent are paying $50 or less per month. Despite that, the Kaiser survey showed, a large percentage of people were unaware they received subsidies, even though it often meant the difference between a plan costing them hundreds of dollars per month, versus a bill in the double digits. Read MoreNew rules bother employers—Obamacare not as much

The finding that only 49 percent of all federal exchange enrollees believed they were getting a subsidy had a fairly large margin of error, of plus or minus 8 percent. But Levitt noted that while the true figure "may be somewhat more or somewhat less...still there's lots of people that don't realize they're getting subsidies."