However, that doesn't mean we can't come up with some agreed upon generalizations.
Who's the 'we'? Do you have a mouse in your pocket? Does 'we' mean, you and the ditto heads? You and the Ayn Rand fan club? If 'we' is you and me, I'll have to warn you about the most I'm willing to generalize about the founding fathers is that they were white men of respectable backgrounds who were representatives of their states. Also, many of them were lawyers, some of them were slave owners. Otherwise they were a diverse group who fought fiercely over the role and responsibility of government (both federal and state for that matter). Hamilton's Report on Manufactures is very clear about what that founding father intended about the 'general welfare clause'.
The wikipedia article has this under 'Opposition to the Report':
Leading opponents of Alexander Hamilton's economic plan included Thomas Jefferson (until later years) and James Madison, who were opposed to the use of subsidy to industry along with most of their fledgling Democratic-Republican Party. Instead of bounties they reasoned in favor of high tariffs and restrictions on imports to increase manufacturing; which interestingly was favored by the manufacturers themselves who desired protection of their home market. Although the Jeffersonian stance originally favored an "agrarian" economy of farmers, this changed over time to encompass many of Hamilton's original ideas, while "the Madison administration helped give rise to the first truly protectionist tariff in U.S. history."
I bring this up for two reasons, a to show more graphically just how different these founding fathers differed and to infer the idea that Jefferson was all over the map with his opinions. The man who wrote the Declaration of Independence wasn't even invited to the constitutional convention, he did not sign it nor did he participate in its first congressional session, as he was away in Paris as the minister to France and attempting to negotiate an end to various British claims (also 'hanging around' with a married woman, and later his deceased wife's slave half sister). Madison, who had also 'beat out' Jefferson for the all but the preamble of the VA constitution, was largely very quite about 'what he meant' when he wrote it, I researched it once and found only three quotes that mostly seemed to be against a broad interpretation of the 'general welfare clause'. Which might seem to be 'good news' for your cause, but as I remember it one of them basically claimed that it was 'copied over from the Articles of Confederation by accident' (not a direct quote, I'm too lazy too look, but I did once research it well) and all of them weren't statements of policies, but a few lines in private correspondence, after his two terms in the White House. Not exactly the stuff of case law and I believe that he wanted it that way. In fact several thing for which he championed were voted out, including establishment of a national university, export taxes and rules governing national elections, which of course are not exactly the ideas of a extremely limited government.
Let me ask you this, if the federal government was not intended to be bound by the Constitution, then what was the point of writing it in the first place?
Huh, I thought what we were talking about how the Constitution was interpreted, why would you ask that leading question?
It's interesting that even after agreeing with me on much of it, you still insist on making generalities about the framers. I'll note that there were only six people who signed both documents (George Read, Roger Sherman, Benjamin Franklin, Robert Morris, George Clymer, and James Wilson), which further diversified 'the founding fathers'. The people who were at the Constitutional Convention are usually referred to as 'The Framers', which (as I mentioned before) did not include Thomas Jefferson, even if his work on the VA Constitution seemed to show up in it. To me the people who use his words to present some idea of a 'Jeffersonian Democracy' as being the intentions of 'the founding fathers', is full on ass hattery, which ignores the political realities of the time, seeming forgets how the man actually governed (even he thought that his Louisiana purchase was unconstitutional, but he did it anyways), and even forgets the various lessons learned. I have no idea why they get away with it.
A related note, I read up on the Madison and the Constitutional Congress, Jefferson and the Constitution and Jeffersonian Democracy
I'll leave you with this quote of Thomas Jefferson in 1789, from a private letter to James Madison:
I set out on this ground which I suppose to be self evident, "that the earth belongs in usufruct to the living;" that the dead have neither powers nor rights over it. The portion occupied by an individual ceases to be his when himself ceases to be, and reverts to the society...
This principle that the earth belongs to the living and not to the dead is of very extensive application and consequences in every country, and most especially in France. It enters into the resolution of the questions Whether the nation may change the descent of lands holden in tail? Whether they may change the appropriation of lands given antiently to the church, to hospitals, colleges, orders of chivalry, and otherwise in perpetuity? whether they may abolish the charges and privileges attached on lands, including the whole catalogue ecclesiastical and feudal? it goes to hereditary offices, authorities and jurisdictions; to hereditary orders, distinctions and appellations; to perpetual monopolies in commerce, the arts or sciences; with a long train of et ceteras: and it renders the question of reimbursement a question of generosity and not of right. In all these cases the legislature of the day could authorize such appropriations and establishments for their own time, but no longer; and the present holders, even where they or their ancestors have purchased, are in the case of bona fide purchasers of what the seller had no right to convey.
Who knew that TJ was into socialist redistribution?