Just remember that the "general welfare" clause is not actually a clause in the constitution confering responsibility or power. It is in the preamble, providing a justification for the powers granted to the federal government by the operative clauses of the constitution.
In other words, it is a goal, a goal that the founders believed could be acheived by granting limited powers to the government.
The commerce clause is an actual operative clause.
Not exactly:
Article I.
Section. 8. The Congress shall have Power To lay and collect Taxes, Duties, Imposts and Excises, to pay the Debts and provide for the common Defence and general Welfare of the United States; but all Duties, Imposts and Excises shall be uniform throughout the United States;
However, the founders clearly articulated that even the general welfare clause should never be construed as to expand the powers of Congress beyond the narrow limitations that the Constitution placed on it.