They do have the power to spend. It simply isn't a power to spend on whatever they feel like.
No, it's the power to spend only to pay the debts and provide for the common defense and general welfare of the United States.
I'm aware of Madison's views. However, although he's sometimes called the "Father of the Constitution," he didn't write the document alone. It was a compromise among competing interests and ideas, and Alexander Hamilton -- who was diametrically opposed to Madison on this issue -- had at least as much input into its final form as Madison did.
Here's another bit of evidence, besides common sense and the interpretations by the Supreme Court. It would have been perfectly possible to create a much more limited tax-and-spend power that did precisely what you are saying this one was supposed to do. We find a good example in the Confederate Constitution, which is almost identical to the U.S. Constitution but in which a few passages were rewritten, and this was one of them:
"The Congress shall have the power . . . To lay and collect taxes, duties, imposts, and excises for revenue, necessary to pay the debts, provide for the common defense, and carry on the Government of the Confederate States; but no bounties shall be granted from the Treasury; nor shall any duties or taxes on importations from foreign nations be laid to promote or foster any branch of industry; and all duties, imposts, and excises shall be uniform throughout the Confederate States."
Note that here, we find again an implicit understanding that the power to tax is also the power to spend, but both are limited much more strictly than in the U.S. Constitution. First, the Congress is authorized to tax (and spend) to pay the nation's debts and provide for the common defense, but beyond that only to "carry on the government," to which the most likely interpretation is "do everything else authorized in this document." And second, a specific restriction is applied involving promoting industry.
If the intent of the framers was to empower Congress only to tax and spend sufficiently to carry out the other enumerated powers, that would have been so stated. It was not difficult to put into words, and these were highly literate men, some of whom were accomplished legal draftsmen. That they did not do this means that they did not intend to.
We sometimes forget that the constitutional convention was called not to limit an oppressive government but to strengthen a government that was so weak and inept it could not get the job done. Limitations were placed in the document because it is unthinkable among liberals that government be created without such limitations. They are necessary for the protection of liberty. But the idea was to create a
strong government, not a weak one, and the framers included some very powerful empowering language, as well as restraints.