The words "general welfare" appear in the first sentence of the Constitution.
"We the people... in order to promote the general welfare...establish this constitution."
It explains why the Constitution was written.
The place where the people delegate limited powers to the Congress is in Article I, Section 8. There is a list of the only 20 powers Congress has been granted by the people. There are no powers delegated which are related to the provision of healthcare.
The Bill of Rights are a list of further restrictions on those 20 powers. If you read the preamble to the Bill of Rights it will tell you so. (The BOR are not a list of rights granted to the people).
The BOR say things like: "Congress shall make no law...", "...shall not be infringed", "...shall not be violated" which makes clear that it is the people telling the federal government what they cannot do.
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