The Founders believed in local government, but recognized the need for a federal government for certain things. From the Federalist Papers:
The powers delegated by the proposed Constitution to the federal government are few and defined. Those which are to remain in the State governments are numerous and indefinite. The former will be exercised principally on external objects, as war, peace, negotiation, and foreign commerce; with which last the power of taxation will, for the most part, be connected. The powers reserved to the several States will extend to all the objects which, in the ordinary course of affairs, concern the lives, liberties, and properties of the people, and the internal order, improvement, and prosperity of the State.
The operations of the federal government will be most extensive and important in times of war and danger; those of the State governments in times of peace and security. As the former periods will probably bear a small proportion to the latter, the State governments will here enjoy another advantage over the federal government. The more adequate, indeed, the federal powers may be rendered to the national defense, the less frequent will be those scenes of danger which might favor their ascendancy over the governments of the particular States.
If the new Constitution be examined with accuracy and candor, it will be found that the change which it proposes consists much less in the addition of NEW POWERS to the Union than in the invigoration of its ORIGINAL POWERS. The regulation of commerce, it is true, is a new power; but that seems to be an addition which few oppose and from which no apprehensions are entertained.
– Madison, Number 45