"The right to be free from federal regulation is not absolute, and yields to the imperative that Congress be free to forge national solutions to national problems, no matter how local -- or seemingly passive -- their individual origins"
there is already Supreme Court precedent that allows the Fed to regulate the commerce of a private entity.
Wickard v. Filburn, 317 U.S. 111 (1942), was a U.S. Supreme Court decision that recognized the power of the federal government to regulate economic activity.
A farmer, Roscoe Filburn, was growing wheat for on-farm consumption. The U.S. government had established limits on wheat production based on acreage owned by a farmer, in order to drive up wheat prices during the Great Depression, and Filburn was growing more than the limits permitted. Filburn was ordered to destroy his crops and pay a fine, even though he was producing the excess wheat for his own use and had no intention of selling it.
The Supreme Court interpreted the United States Constitution's Commerce Clause under Article 1 Section 8, which permits the United States Congress "To regulate Commerce with foreign Nations, and among the several States, and with the Indian Tribes". The Court decided that Filburn's wheat growing activities reduced the amount of wheat he would buy for chicken feed on the open market, and because wheat was traded nationally, Filburn's production of more wheat than he was allotted was affecting interstate commerce. Thus, Filburn's production could be regulated by the federal government.
heres another interesting ruling from 2011:
Supreme Court Commerce Clause | Supreme Court ruling hints of difficulty for Obama insurance law foes - Los Angeles Times
The Supreme Court may not be so anxious to rein in Congress' broad power to pass regulatory laws under the Constitution's commerce clause, the key point of dispute in the pending court battles over President Obama's health insurance law.
By a 7-2 vote, the justices turned down a constitutional challenge to a 2002 law that makes it a federal crime for a felon to have body armor or a bulletproof vest.
The majority's decision, rendered without comment, could make it more difficult for those challenging health insurance reform to win court orders overturning parts of the new law.
"The federal power claimed is the authority to regulate anything — from the possession of French fries to the local theft of a Hershey's Kiss," argued lawyers for Cedrick Alderman, a Seattle man who appealed the body-armor law.
But the lower courts had upheld the law. The Supreme Court considered the appeal over several monthsbut rejected it Monday in Alderman vs. United States.
Alderman's appeal concerned only whether Congress had the power to enact a law regulating the possession of a product — in this instance, body armor.
based on precedent such as this, there is a high likely hood that the court will uphold the mandate.