THE ADMINISTRATION'S budget is less supportive of state and local government than it was made out to be. The text is full of praise particularly for the states as imaginative laboratories better able than the federal government to judge what their populations need and more adept at providing it. As proof of the president's adherence to this article of faith, the budget proposes that $15 billion a year in federal programs (out of a list of $20 billion offered up) be blended into a grant to the states to do with mainly as they please.

That's an old and, in the present circumstances, bad idea; the federal government has no business sharing revenue that covers only four-fifths of its own costs. But even on its own terms, this latest formulation of the new federalism was an obvious afterthought. Of the $20 billion, $5 billion (scheduled to rise to $8 billion by 1996) is now given to the states to help pay the administrative costs of Medicaid, food stamps and Aid to Families with Dependent Children. There would be no reduction in the states' administrative responsibilities; they would still have the same costs to cover. Another $2 billion is in grants to build sewage treatment plants; the program is already scheduled to be phased out and the construction function to be turned back to the states in the next few years.

Other prospects on the list are programs the administration would like to phase down or out, and/or programs in which the state and local recipients already have maximum flexibility. Grants to help the poor pay heating bills would be included -- but the budget calls for cutting them from $1.7 billion this year to about $300 million in fiscal 1996. Community development block grants, another nominee, would be held constant at about $3 billion a year; by 1996 they would have lost more than a fifth of their value to inflation. Most of these development grants now go directly to local governments; relatively few conditions are attached. That is one of the reasons why the mayors swear by the program -- while the lack of control has been a federal criticism of the grants in the past. The mayors say the president's proposal would create a layer of (state) bureaucracy at their expense.

A fourth of the $20 billion is made up of unspecified subsidized housing programs; the day the budget was sent up, the housing secretary said he had no idea what the budget office was talking about. Meanwhile: The budget projects that total aid to state and local governments, having fallen in real terms in the Reagan years, will start back up again. But the increases are such that the states will have to pay to get them: The main increases forecast are in Medicaid, which is now more than a third of all federal aid to state and local governments and whose cost the states must match. Congress has expanded the program in recent years to reach more of the poor; the governors say they can't afford the generosity. The administration also proposes that highway spending be increased, but under different matching formulas; the states would have to pay a larger share.

The Medicaid expansion and new cost sharing for highways both are good ideas. But in the fiscal terms that define federalism, the states will be no better off. The big question is always: Which functions should the federal government take over, which leave to the states. That's no better answered in this budget than before.