THE GOVERNORS wound up their annual meeting yesterday with a firm reminder that their continued support for the Reagan budget policies will depend on some sign that the newest version of a "New Federalism" is more than a plan to unload federal responsibilities on already strained state budgets. Thus far, the governors have given much more than they've gotten--federal grants to states will drop by as much as a third in purchasing power next year, while the amount of newly flexible money included in block grants is barely enough to offset last year's $2.3 billion loss in state revenue sharing.

The governors revived proposals for a bold swap of federal and state responsibilities. The governors propose a complete state takeover of some programs like education in return for full or greater federal assumption of the costs of the relatively uncontrollable welfare and Medicaid programs. The governors argue that only complete federal withdrawal from some areas can produce substantial administrative savings. States and localities already pay over 90 percent of education costs so that the bureaucratic price of federal involvement in education is especially high.

The governors are also right that the responsibility for meeting the basic needs of the nation's poor is properly a federal one. States have little control over the number of poor people in their jurisdiction. When they try to control caseloads by limiting benefits, the result is to foster an unhealthy concentration of the needy in more generous, though not necessarily more affluent, areas. Federal policies may also add to local welfare burdens--witness the impact of weak immigration and refugee policies on Florida and other coastal and border states, or the new threat to New York of a Puerto Rican influx arising from the severe cuts in aid to Puerto Rico. Nor is any state immune from the double blow of a downturn in the local economy that brings rising needs and falling state revenues.

Working out the terms of a federal-state swap would not, however, be an easy matter. The administration would clearly like to shift more, not less, of the welfare and Medicaid burden to the states. There is also good reason for concern that some states, given full control over education policy, would not choose to continue the compensatory education programs that have shown solid payoffs for the nation in recent years. Nor should anyone be sanguine about turning over welfare policy to the current stewards of the federal welfare establishment. Then there are all those nasty--and costly-- little technicalities. Welfare and Medicaid benefits vary greatly from state to state--last year Texas paid $140 monthly to a welfare family of four while California paid $563. Average Medicaid payments for an old person in Connecticut run about seven times as high as in West Virginia.

Which standard would prevail in a federal take-over? What if a state's share of education and assumed programs didn't happen to match its share of welfare and Medicaid costs?

There is no simple way to develop a federal-state system that serves not only the perceived needs of each state but also the needs of the nation as a whole. The governors are right, however, to want a stronger say in setting the new terms of the partnership.