In short, as Madison argued, Congress derives no power from the general welfare clause, which merely serves to limit Congresss power to lay and collect taxes. Congress can only do so for purposes of common defense or general welfare, in the service of the powers granted to it elsewhere in Article I.Second, Necessary and Proper gives Congress the power to make all laws necessary and proper for carrying into execution the foregoing powers, and all other powers vested by this Constitution in the government of the United States. Like the general welfare clause, this clause was not a stand-alone grant of power to Congress. Rather, it authorizes Congress to make laws that are necessary (and also proper) to make the other grants of authority in Article I effectual.
In other words, the necessary and proper clause cannot itself authorize national public health insurance. One would have to show that national public health insurance is necessary and proper to execute some other power granted in the Constitution. This puts the proponents of nationalized healthcare back where they started.
Lastly, proponents might argue that national health insurance is part of Congress power to regulate commerce among the several states. While progressives have often used this clause to expand the federal government, it does not apply especially to the creation of a national health insurance, because to create and engage in commerce is not the same thing as regulating commerce among the several states.