The arguments track the Obama administration's arguments before lower courts. In this brief, the DOJ argues that the requirement that uninsured people purchase coverage (with government subsidies) is Constitutional both under Congress' power to regulate interstate commerce and because the mandate functions as a tax, which the Constitution provides the Congress wide authority to levy.
The argument suggests very strongly that if the Supreme Court strikes down the mandate, they'll also have to strike provisions in the law requiring insurance companies to sell coverage to everybody, and preventing them from pricing sick individuals out of the market.
This is the first in a series of briefs the administration will file with the Supreme Court. The Court will hear oral arguments in March and is expected to rule next summer, in the heart of election season.