It's overtly implied in the 4th Amendment.
Implied yes! Directly stated NO! Case law was needed to provide for a constitutional right to privacy!
Griswold v. CT and
Roe v. Wade established privacy as protected by the constitution!
In
Griswold you have the famous Douglas wrote the famous lines that "a right to privacy can be found in the penumbras (shadows) of the bill of rights!" Specifically, 1st (assembly), 3rd amendment (not housing soldiers), 4th (unlawful search and seizure), 5th (Due process clause and Taking clause) and 9th amendment (rights of the people)!
The point is just because the constitution doesn't state it doesn't mean it can't be inferred. Ask any libertarian and he will hold scared right to privacy, but he WILL NOT be able to show you direct wordage in any part of the constitution that states, "We as American citizens have a
RIGHT TO PRIVACY!"
Therefore even thought the constitution doesn't mention health care there are many parts of the constitution were healthcare can be inferred.
Example:
Constitution Preamble:
...provide for the common defense, promote general Welfare, and secure the Blessing of Liberty in ourselves and our Posterity...
Section 8 Clause 1 (Powers Granted to Congress):
"The Congress shall have Power to...provide for the common defense and general Welfare of the United States.
Amendment V:
No person shall be denied
life,
liberty or property without due process of the law.
Amendment XIV:
Due Process Clause redux, Privilege and Immunity Clause and Equal Protection Clause.
The point is if your argument is that the state shouldn't provide healthcare (something I am not sure I don't support), because that is what the constitution doesn't directly provide for it, then you are wrong. Get a different argument, because there are many rights that we as Americans cherish that are stated directly in the constitution, such as a right to privacy, but are found in the penumbras of the constitution.