No serious Constitutional Law scholar has argued that healthcare reform (in any of the currently proposed formats) is unconstitutional. Some conservative commentators, however, have tried unsuccessfully to float the argument.
Yes, Virginia, Healthcare Reform Is Constitutional
On August 22, David Rivkin Jr. and Lee A. Casey, two rightwing attorneys, argued in the Washington Post, that healthcare reform violated the Constitution. Their argument, however, only captured the hearts of conservatives desperate to find a good good reason to oppose healing the sick.
Today, the conservative blog Hot Air tried to revive the argument by posting footage of Senator Mark Warner explaining why healthcare reform is constitutional. Although the video link no longer works, the summary by Hot Air states that Warner cites to the Commerce Power as authority for healthcare reform. This is exactly correct, but I would add the Taxation and Spending Powers as well. I have thoroughly analyzed this issue in a prior blog post (and in the comments section to that post). Even conservative Constitutional Law professors have made similar arguments (see the post I linked).
Absurdity of the Question
It is absolutely absurd to ask whether the constitution specifically or explicitly allows Congress to regulate or reform healthcare. The Constitution speaks broadly and ambiguously. Only a few provisions are specific and beyond dispute (like the age requirement for presidents and members of Congress).
The Constitution does not specifically or explicitly authorize the creation of the Air Force or Medicare, nor does it discuss the federal prosecution of crack cocaine possession. And the "Framers" certainly did not specifically contemplate airplanes, prescription drug and hospital plans for seniors, or crack cocaine because these things were not realities when they wrote the Constitution.
If conservatives only believe Congress can regulate things that are explicitly mentioned in the actual text of the Constitution, then they should essentially advocate the abolition of the federal government. At a minimum, they should seek the immediate repeal of laws banning partial-birth abortion and kidnapping; the Constitution does not mention children or abortion.
Also, as many students of high school and college civics classes know, Article I of the Constitution contains the "necessary and proper" clause, which endows Congress with unenumerated powers that are needed to carry out its expressly delegated powers. In the very first case interpreting this provision (McCulloch v. Maryland), the Supreme Court rejected the narrow interpretation offered by anti-federalists.
Many of today's conservatives pretend that the Necessary and Proper Clause does not exist or that courts can only interpret it conservatively. Nothing in the history of the clause or the Court's interpretation of it compels an exclusively narrow interpretation.
Finally, I find it ironic that the GOP's so-called Bill of Rights for Seniors pretends to offer protection for Medicare, while conservatives have repeatedly asserted that healthcare reform violates the Constitution. If Congress lacks the power to pass healthcare reform, then it probably lacks the power to create Medicare, which conservatives claim to support. The inconsistencies are absolutely dizzying.