Mike Sacks at HuffPo reports that the oral arguments will take place over 3 days at the end of June - this is the most important day:
The main event will be on Tuesday, March 27, when the Court will take up the constitutionality of the health care law's minimum coverage requirement. That provision, commonly called the individual mandate, requires virtually all Americans to purchase health insurance or pay a penalty. The Court has set aside two hours for argument over whether Congress' passage of the individual mandate exceeded the legislature's powers to regulate interstate commerce or lay and collect taxes under Article I of the Constitution.