In the first administration Jefferson told Hamilton there could be no Bank of the US because the Constitution did not explicitly enumerate it. Hamilton responded that the Constitution could not be expected to enumerate everything (kind of like our rights in it). As the stories go, Jefferson wasn't even a Framer as he was in France when the Constitution was hammered out, whereas Hamilton was a Framer. So really if we are going to talk about what the Framers intended, why not tell the whole story?
Even from afar the work jefferson had already done in shaping this nation was more of an influence that that of Hamilton who was a two bit player at the convention.
But why debate those two when Madison is the father of the Constitution?
And what did Madison say?
"If Congress can employ money indefinitely to the general welfare,
and are the sole and supreme judges of the general welfare,
they may take the care of religion into their own hands;
they may appoint teachers in every State, county and parish
and pay them out of their public treasury;
they may take into their own hands the education of children,
establishing in like manner schools throughout the Union;
they may assume the provision of the poor;
they may undertake the regulation of all roads other than post-roads;
in short, every thing, from the highest object of state legislation
down to the most minute object of police,
would be thrown under the power of Congress.... Were the power
of Congress to be established in the latitude contended for,
it would subvert the very foundations, and transmute the very nature
of the limited Government established by the people of America."
and
"If Congress can do whatever in their discretion can be done by money, and will promote the General Welfare, the Government is no longer a limited one, possessing enumerated powers, but an indefinite one, subject to particular exceptions. (James Madison, Letter to Edmund Pendleton, January 21, 1792 Madison 1865, I, page 546)"
Commentators virtually agree on the answer Madison proposed and defended in Federalist 41, namely, that the general welfare clause is neither a statement of ends nor a substantive grant of power. It is a mere "synonym" for the enumeration of particular powers, which are limited and wholly define its content. From this answer, it follows that the primary meaning of the national dimension of the federal Constitution is limited government, understood as a government with a limited number of powers or means.