WHITE HOUSE aides lost no time in relieving the nation's governors of any hope they may have had that the administration would agree to a swap of responsibilities--the states taking over the full cost of education, transportation and the like in return for federal assumption of welfare and medical assistance programs. The administration's agenda, on the contrary, calls for giving the states more, not less, responsibility for everything, including welfare and Medicaid--probably in the form of a block grant with a lid on federal contributions.

The governors were naive to expect anything else. The simple arithmetic of budgets, taxes and deficits makes it obvious that the administration will be seeking over the next couple of years to unload the great bulk of present federal responsibilities, other than defense and Social Security, onto someone else --and the governors are first in the likely receiving line.

It is true that Congress courageously enacted both tax and budget cuts before taking its summer vacation. Both the administration and Congress, however, were a great deal more courageous on the tax than on the budget side. The enacted tax cuts represent a revenue loss estimated at $280 billion over the next three years. The budget cuts come to only $130 billion, less than half the tax loss over the same period. If the economy doesn't do as well as the administration hopes, the gap will be still larger. What this means, as President Reagan acknowledged in signing the tax and budget bills, is that the administration will have to seek much larger additional budget cuts than it had previously forecast. In fact, over $100 billion in budget cuts on an annual basis may well be needed to bring the budget into balance by 1984--three times as much as the $35 billion already enacted.

Where will most of that money come from? Almost surely from the remaining $85 billion or so that the federal government now transfers to states and localities for education, housing, highways, welfare, revenue sharing and so on. With defense expenditures already scheduled for large increases, soaring interest costs on the federal debt and basic Social Security and veterans' benefits more or less inviolate, there is simply no place else to go.

For the same reasons, there is little hope that the federal government will be able to transfer any of its remaining tax authority to the states even beyond 1984. Under the tax bill just signed into law, federal revenues will go into an even steeper nose dive then because many of the special tax breaks in the legislation don't come into full effect until after 1984--a gimmick used in the congressional markup to give some aura of restraint to the exercise.

This amounts to an enormous reversal in American social policy. Over the last decades, the nation has moved steadily toward reducing some of the wide disparities in income, nutrition, educational opportunities and general living standards among citizens in different regions and localities. Most people have found that progress healthy, if far from complete. In the process, no doubt, states and localities have lost much control over their local destinies, and some correction of this seems in order. It is, however, far from clear that the governors--or the people they represent--are ready or eager for a return to the days when the basic needs of citizens depended, critically, on the wealth and generosity of the states and localities in which they resided.