The Constitution does not address health care in any fashion. You cannot equate the absence of language regarding an activity with its prohibition. Nowhere in the Bill of Rights does it say "the following 10 rights are the only rights enjoyed by Americans".
The Constitution, as I said, is not a document that grants rights. It is a list of delineation of responsibilities and prohibitions on the federal government. Universal healthcare is not a responsibility of the federal government, and it is enjoined from interfering in the power which resides with the states.
The Constitution says nothing about cars, airplanes, or baseball. Should we amend it before we can drive, fly or go to the game?
You do not understand (or you are intentionally disregarding) the fact that the Bill of Rights is actually nothing of the sort. It does not grant rights, it prohibits the federal government from infringing on certain rights. Therefore, one does need government permission or an amendment to enjoy a game of baseball, but the government cannot infringe on the (for example) right to freedom of speech. The Bill of Rights doesn't say what we citizens have rights to do, it says what the federal government cannot do.
We call the most basic of those rights 'civil liberties' and the government is bound to protect them. Healthcare has not been defined as one of those rights to which we are entitled, and as such, the federal government has neither the mandate nor the power to grant it; especially when it interferes with one of our most basic human rights, the 'right to be left alone'.
If we as a nation decide to amend the constitution to define health care as a basic right, then we also empower the federal government to provide it. If we do that, then I have no qualms with nationalizing our health care system, but I would hope it would be done by utterly dismantling the broken system we now have and replacing it with something that is designed from the ground up to be run by the government.
If we as a nation do not make such a determination, and do not so amend the Constitution, then I want the federal government to get out of my wallet, get out of my life, and leave me alone. This is a fundamental right - and a defined one - that liberals seem to have a serious problem grasping. I have no desire to run your life, but you can't seem to get over your need to control mine.