"They" - the folks that made our Constitution - were 55 delegates (and over 1500 ratified the Constitution), so they thought a lot of different things. When we look at some core architects and founders, namely Madison, Jefferson, and Hamilton, we see a clear picture: some founders insisted they meant what they said when they said it.

It didn't take long for the interpretation debate to occur. Within just a few short years of signing our Constitution, Hamilton set out to build the Treasury. Jefferson felt he was going beyond the enumerated powers - those specifically granted to the federal government by the Constitution - and that all non-enumerated powers were the right of the states and the states alone. Madison agreed. Hamilton felt implied powers existed, which is (arguably) outside the scope of the defined language. So we see very strong responses, particularly from Jefferson, that indicate support for strict interpretation - what would essentially later be "originalism" (but that term would be foreign to the founders). So from TJ's corner, they wrote a document and the words are right there, and they express the whole truth. If you want to know, look at what they wrote in plain (to them) English.

Hamilton supported a living document. One that would ebb and flow with the desires and needs of the federal authority. The General Welfare provision provided all he needed to authorize such alteration. Since you mentioned the Federalist Papers, Madison spoke his mind in [#41] (https://avalon.law.yale.edu/18th_century/fed41.asp) (in 1788, even before the great bank debate);

Some, who have not denied the necessity of the power of taxation, have grounded a very fierce attack against the Constitution, on the language in which it is defined. It has been urged and echoed, that the power "to lay and collect taxes, duties, imposts, and excises, to pay the debts, and provide for the common defense and general welfare of the United States,'' amounts to an unlimited commission to exercise every power which may be alleged to be necessary for the common defense or general welfare. No stronger proof could be given of the distress under which these writers labor for objections, than their stooping to such a misconstruction. Had no other enumeration or definition of the powers of the Congress been found in the Constitution, than the general expressions just cited, the authors of the objection might have had some color for it; though it would have been difficult to find a reason for so awkward a form of describing an authority to legislate in all possible cases. A power to destroy the freedom of the press, the trial by jury, or even to regulate the course of descents, or the forms of conveyances, must be very singularly expressed by the terms "to raise money for the general welfare."

Then later says;

For what purpose could the enumeration of particular powers be inserted, if these and all others were meant to be included in the preceding general power? Nothing is more natural nor common than first to use a general phrase, and then to explain and qualify it by a recital of particulars.

And concludes;

But what would have been thought of that assembly, if, attaching themselves to these general expressions, and disregarding the specifications which ascertain and limit their import, they had exercised an unlimited power of providing for the common defense and general welfare? I appeal to the objectors themselves, whether they would in that case have employed the same reasoning in justification of Congress as they now make use of against the convention. How difficult it is for error to escape its own condemnation!

He was absolutely against deviation from the specifics outlined. However, the first quote starts out;

A system of government, meant for duration, ought to contemplate these revolutions, and be able to accommodate itself to them.

He was talking about taxes, specifically import duties, but was in a larger sense reflecting on the changing dynamic of American industry, marching from agriculture to manufacturing, and commenting on the need to be able to change with the general will or benefit of the people.

As for Jefferson, he wrote in 1791;

To lay taxes to provide for the general welfare of the United States, that is to say, “to lay taxes for the purpose of providing for the general welfare.” For the laying of taxes is the power, and the general welfare the purpose for which the power is to be exercised. They are not to lay taxes ad libitum for any purpose they please; but only to pay the debts or provide for the welfare of the Union. In like manner, they are not to do anything they please to provide for the general welfare, but only to lay taxes for that purpose. To consider the latter phrase, not as describing the purpose of the first, but as giving a distinct and independent power to do any act they please, which might be for the good of the Union, would render all the preceding and subsequent enumerations of power completely useless.

It would reduce the whole instrument to a single phrase, that of instituting a Congress with power to do whatever would be for the good of the United States; and, as they would be the sole judges of the good or evil, it would be also a power to do whatever evil they please.

Madison and Jefferson were lock step - the Constitution gave specific powers in specific words and that's what it meant. No two men of the era made such a strong claim (though many followed them), and even though Jefferson was in France when the document was drafted, Madison was quite involved in its construction and ratification, (properly) earning the nickname "Father of the Constitution".

Typos for the E!