STATE AND LOCAL governments have been studying the administration's 1984 budget proposals with understandable concern. These governments are the vehicles by which many federal programs--everything from environmental clean-up to welfare benefits--are delivered to the public.

States and cities were successful last year in persuading Congress to reject much of the $10 billion in grant cuts that the administration had proposed. Still, the cuts that were made--combined with the devastating effect of the recession on revenues-- have put these governments in a tight bind. In the past two years, almost all of them have been forced to cut programs, lay off workers or raise taxes. Many have done all three. Most are still cutting services and raising taxes to fit within this year's budget, and they are in no mood for further federal aid cuts.

On its surface the president's 1984 budget "freeze" promises better treatment than his earlier proposals. But state and local governments have learned to be suspicious of administration offerings. A study released last week by the National Conference of State Legislatures and the National Governors Association observes that while budget totals may be frozen, a lot is going on under the ice.

Some categories of spending are scheduled to rise. The 5-cent highway tax rise will boost spending on interstate and primary highways--although the 1 cent earmarked for mass transit has been offset by a reduction in other transit aid. Medicaid spending authority looks as if it's in for a big increase, but this is just an accounting change (soaring medical prices will actually force cuts in service). Past authorizations will make subsidized housing construction rise--but future money has been cut off.

Needy people--a group that the recession has brought increasingly to the attention of state and local governments--are in for further cuts. Despite the increase in the number of poor, spending for programs to help them would be cut by another $2.2 billion, bringing the purchasing power of these programs to 17 percent below the 1981 level.

The administration is no longer proposing a "big swap" of responsibilities. Rather, it is asking for another round of "block grants." With these consolidations of child welfare, family planning, health, education and other social programs would come funding cuts from 10 to 20 percent. These cuts--together with the fact that the block grant set up last year for community services has now been earmarked for extinction--have made the states far less enthusiastic about the advantages of greater "flexibility."

There is no easy way out for state and local governments caught in the squeeze between the federal government's desire to lighten its domestic responsibilities and citizens' pressure for maintaining public services. Greater efficiency may afford some relief, but without the equalizing effect of federal aid, it is likely that the citizens of less prosperous jurisdictions will have to accustom themselves to a poorer level of community services.