But when the potential fallout is explained, most say it would hurt the country and they would look to Congress or the states to fix it.
Although recent oral arguments before the Supreme Court got national media attention, 53 percent said they were unfamiliar with the case, according to a Kaiser Family Foundation poll released Thursday.
Opponents of the law say its precise wording allows the government to subsidize coverage only in states that set up their own insurance markets, or exchanges. Most have not done so, defaulting to the federal HealthCare.gov.
When people were asked about the potential consequences of a Supreme Court ruling to deny financial assistance in states with federally-run insurance markets, 62 percent said that would have a negative impact on the country.
"The public is not making a legal judgment," said Drew Altman, CEO of the foundation. "When it's explained to them that some people will get help depending on whether the state or the federal government runs the marketplace, it does not seem fair to people. It does not make sense to the majority."
The Kaiser foundation is a nonpartisan information clearinghouse on health care issues. The poll is the latest installment in its survey series, which has tracked public opinion since the inception of Obama's overhaul
Overall, it found Americans remain divided over the health care law, which offers subsidized private insurance to people who don't have access to it on the job, plus expanded Medicaid coverage for low-income adults in states that accept it. Forty-three percent view it unfavorably, while 41 percent have a favorable opinion.
The Supreme Court case is known as King v. Burwell. Supporters of the law argue that while the wording of particular provisions may be confusing, the clear intent was to provide benefits in all states.
No one knows how the court will rule. It could side with the Obama administration, or strike down subsidies that more than 8 million people are receiving.
The outcome seems to hinge on the votes of Chief Justice John Roberts and Justice Anthony Kennedy. While Kennedy asked sharp questions of both sides during oral arguments, Roberts said little. Kennedy voted against the law in the 2012 case challenging its constitutionality. Roberts provided the key vote to uphold it.
If the Supreme Court invalidates subsidies for people in some three-dozen federal marketplace states, most poll respondents (65 percent) said Congress should pass a law so residents of all states can get financial assistance.
But partisan divisions foreshadow problems. While 81 percent of Democrats and 67 percent of independents favored a congressional fix, 56 percent of Republicans opposed rescuing what detractors call "Obamacare."
When people in the states potentially affected were asked how their governors and state legislators should respond, 69 percent said their states should create their own markets so residents could keep receiving help. That view cut across party lines.
If the court rules for the law's opponents and against the Obama administration, "Democrats are likely to have the public on their side," Altman said. "They'll be making a fairness argument ... and the poll does show the public views this as a fairness question."
But he said Republicans "will have cards to play" because the highest court in the land will have just discredited the law.
The telephone poll of a nationally representative random sample of 1,503 adults was conducted from March 6-12. The Supreme Court heard arguments on March 4. The margin of sampling error is plus or minus 3 percentage points for the full sample.
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(Photo: Pablo Martinez Monsivais, File/AP Photo)