The law, dubbed ObamaCare, passed in 2010, requires all Americans to obtain health insurance or face a penalty fine.
But conservative opponents of the president say that “mandate” is illegal under the terms of the US constitution.
The justices are expected to rule on Thursday, and could cut the mandate or strike down the whole law.
The debate over healthcare is a fiercely polarizing issue in the US, and a verdict either way is expected to have a major impact on the race for the White House.
Barack Obama and Republican Mitt Romney, a former Massachusetts governor, are just five months away from the presidential election.
The president maintains a slender lead in some polls, but is facing a stiff challenge from Mitt Romney and conservative opponents, amid a rocky economic outlook.
Mitt Romney told a rally near Washington DC on Wednesday that if the Supreme Court did not quash the law he would “repeal and replace” the bill if he won the White House.
The bitter debate over the legislation has touched such partisan issues as state and individual rights, federal deficits, end-of-life care, and abortion and contraception funding.
The nine-member Supreme Court has several options.
It could decide that it is too early to rule on the case, as many of the law’s provisions – including the mandate to buy health insurance – do not come into force until 2014.
It could also dismiss the challenge to the mandate on a technicality, ruling that the penalty constitutes a tax lawfully imposed by Congress. Few observers expect the court to choose this option.
The meat of the case concerns the challenge to the individual mandate, which the justices could decide oversteps Congress’ right to regulate interstate commerce.
Analysts say that questioning from several conservative justices during oral arguments at the court in March revealed a deep level skepticism on the bench.
The court could decide to strike down the mandate and send the bill back to Congress to find a way to make the rest of it work. It could also overturn the entire law, ruling that the need to buy health insurance is integral to the legislation.
The Supreme Court is composed of nine justices, five seen as conservatives and four as liberals. It has delivered several divisive wafer-thin majority rulings in recent years, prompting criticism from liberals.
A 5-4 ruling in 2010 known as Citizens United changed campaign finance laws in the US to allow unrestricted fund-raising by independent groups not directly affiliated with candidates.
A recent study by the Pew Research Center found public approval of the court at its lowest level since records began in 1987.
The healthcare law – officially known as the Patient Protection and Affordable Care Act, but commonly dubbed ObamaCare by opponents – was passed in 2009 without a single Republican vote in Congress, and signed into law by President Obama in June 2010.
Polls suggest many Americans would be pleased to see the law overturned.
However, individual elements of the bill are popular, and some people are opposed because they do not think it goes far enough.
The bill has already enabled millions of Americans aged under 26 to obtain health insurance by staying on their parents’ coverage for longer than previously allowed.
Patients with pre-existing medical conditions have also been able to obtain health insurance since the passage of the law.
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