Madison explained it, first

When I first heard the claim that the constitutional power of Congress to impose taxes in order to pay the debts and provide for the common defense and general welfare was (allegedly) an affirmative grant of authority to spend money on whatever Congress considers to further the common defense or general welfare, I traced the history of that clause through the Constitutional Convention, using James Madison's notes on the convention.  As it turns out, it was unnecessary for me to do this, as Madison himself explains exactly what I discovered by doing so, in this letter.

There are two main points that I urge readers to take away from this.  First, the "common defence and general welfare" language is a restriction on the power of Congress to tax -- it may only tax in order to pay the debts of the United States and to provide for the common defense and general welfare, but it is not necessarily empowered to spend on whatever constitutes the common defense and general welfare.  Second, the Articles of Confederation included a similar clause, allowing expenses incurred for the common defense and general welfare to be paid out of a common treasury.  Any theory of interpretation that would just as properly have justified entitlement programs being established under the Articles of Confederation (if they had been) ought to be viewed with suspicion.  (Then, after suspecting that theory of interpretation of being wrong, the person who is considering it ought to reach the conclusion that, yes, such a theory of interpretation must be wrong.  These clauses surely were not meant to give Congress an open-ended power to spend money.)