While the court is focused primarily on the law's individual mandate provision, which requires most Americans to buy health insurance or face financial penalty, the justices could strike down the entire legislation.
Large insurers such as UnitedHealth Group, WellPoint and Aetna will be affected by a decision on the law.
Companies: Microsoft is expected to announce some news related to its own tablet computer Monday at an event in Los Angeles. Shares of Microsoft, which lost 2% in Friday trading, edged lower Monday.
Shares of footwear retailer DSW plunged 11% Monday after it warned that its fiscal second-quarter earnings would come in at 60 to 64 cents a share, far below its previous guidance and a consensus forecast of 76 cents a share.
Shares of Groupon surged 11% after the online coupon site was upgraded by an analyst at Morgan Stanley.
Shares of Facebook continued to rally Monday marking a third straight day of gains.
An article in Monday's Wall Street Journal said decisions by Facebook's lead underwriter Morgan Stanley were responsible for many of the problems with the IPO. Morgan Stanley closed down 3%.
Many of the nation's largest banks -- Goldman Sachs, Citigroup and Bank of America -- also closed lower due to the uncertainty in Europe.
Currencies and commodities: The dollar was little changed against the euro, and higher versus the British pound and Japanese yen.
Oil for July delivery fell 76 cents to $83.27 a barrel.
Gold futures for August delivery fell $1.10 to $1,627.00 an ounce.
Bonds: The price on the benchmark 10-year U.S. Treasury dropped slightly, pushing the yield up to 1.58% from at the 1.57% level reached late Friday.