Many states and localities are barely back on their feet after the deep recession two years ago. Others have hardly recovered at all. Now they must prepare themselves for another round of federal budget cuts that, if President Reagan has his way, will be even deeper than those enacted four years ago.

With all the talk about the federal budget, it's easy to forget that state and local governments administer most of the programs -- from welfare aid to road and sewer building -- that touch so many people's lives. As a result of earlier budget cuts, federal aid for such programs has already lost about 20 percent of its purchasing power in recent years. Deeper cuts in social programs and population losses have cost some areas still more.

Now the administration is proposing almost $40 billion in new cuts for nondefense programs other than Social Security. As budget director David Stockman stresses, these cuts are broadly distributed among all areas of federal spending that aren't sacrosanct. Even so, a large share of the losses would be sustained by people and localities already under great strain.

Some of the cuts -- more than the administration likes to acknowledge -- are aimed directly at low-income people. These include new cuts in Medicaid, children's nutrition programs, welfare for families, summer jobs, job training, aid for needy students, day care and other social services and, especially, public housing and other housing aid. But a still larger group of cuts, aimed at localities rather than directly at people, will also tend to hit hardest on areas with many low-income residents.

Revenue-sharing, for example, is slated for extinction. Although the funds in this program are much too widely dispersed, and the justification is shaky, it does provide especially welcome help to cities with burgeoning poverty populations. So do urban and community development grants, mass- transit subsidies and social service, training and summer job funds. Rural areas would be hit by similar losses in direct aid and far larger losses in the numerous farm-support and loan programs that buoy farmers' income. At the same time, states and localities also would be under pressure to replace some of the welfare and medical benefits that the federal government would no longer pay for.

States and localities where private economies are flourishing -- or where much defense money is spent -- might be able to make up these new losses from expanded tax bases or by raising local taxes. But others would not. The states and localities that would find it hardest to replace their losses would tend to be those with the greatest need for assistance. What a plan.