The preamble to the Constitution states that one of the reasons we the people created the Constitution was to "...promote the general Welfare..."
Article I, Section 8, states, in part: "The Congress shall have Power To...provide for the...general Welfare of the United States..." and that Congress has the authority "...To make all Laws which shall be necessary and proper for carrying into Execution the foregoing Powers..."
So, yes, Congress has the authority to enact universal health care.
All other advanced democracies, other than the United States, consider health care a collective responsibility.