What Does the Constitution Mean By "general welfare"?

This is a little bit of a side issue, but it relates to the administrations efforts to institute health care reform. I was curious about the argument that the federal government does not have the authority to make such reforms under the constitution. The argument is that anything that is not expressly authorized is not allowed. As such, the constitution would have to say something specific about health care for it to be in the purview of the federal government.

The counter argument is that they do have the authority under the general welfare clause of Article 1 Section 8:

The Congress shall have 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; but all duties, imposts and excises shall be uniform throughout the United States;

This is a good article that explains the legislative and judicial history of this clause: SPENDING FOR THE GENERAL WELFARE