Of course, the act is unconstitutional because it is a clear exercise of powers Congress has not been delegated, but we begin with a Court of nine, four of whom make no pretense of following the Constitution. So, where you have five justices who pretend to care what the Constitution says, you need all five to come through.
The usual provision that promoters of federal power cite is the Commerce Clause, which allows Congress to regulate interstate commerce. It has been used to justify acts that a normal person-- you know, someone without a law degree-- would never consider to involve interstate commerce. But in the Obamacare case, Congress (which read the bill, if at all, sometime after it was passed) orders private citizens to purchase a private company's product within that state or else be fined.
As you know, Roberts "authored" the majority opinion, which upheld Obamacare's insurance purchase mandate. The rub is that he ruled that the commerce clause does not justify the act; rather, the penalty paid by non-purchasers is a mere tax. And Congress can tax.
As an aside, there are many non-conspiracy theorists who draw the conclusion that Roberts did intend to strike down the law, and that the "dissent" was actually originally the draft of Roberts' majority opinion. But then someone (ahem) or something got Roberts to change his mind.
Regardless, Roberts was too smart by half. You see, the Constitution's origination clause mandates that tax bills originate in the House of Representatives:
But Obamacare originated
So, now that the DC Court of Appeals has rejected a challenge on this basis, the Supreme Court can hear it if the four dissenters on Obamacare vote to grant certiorari.
Then we'll see how Justice Roberts gets out of this mess. He's already ruled it was not justified by the commerce clause. And the origination clause demands tax bills to start in the House. However it ends up, it is a good thing. Either Obamacare is belatedly but deservedly done away with, or else the corruption of our rulers is further exposed.
** Please don't misunderstand me. I have exactly zero expectation that the U.S. Supreme Court will strike down Obamacare for any reason; the Court is bought and paid for. What I do heartily approve of is seeing the abusers of power get caught in a lie and then being exposed for the charlatans they are to the 14 citizens who still care.