On what grounds is the health-care law being challenged?
Historically, federal courts have interpreted the Commerce Clause to enable Congress to regulate interstate economic activity or noneconomic activity that "substantially affects" interstate commerce. However, plaintiffs assert that Congress cannot direct its Commerce Clause power at one's inactivity. To them, the individual mandate does just that by forcing Americans to spend their money on insurance they may not want.
Further, the states claim that Congress is commandeering traditional state powers under the 10th Amendment, such as regulating intrastate insurance programs.