THE NATION'S governors have become increasingly ill-humored in recent months about the administration strategy of cutting federal spending by shifting its own burdens to statehouse doorsteps. The governors know that a good part of the $30 billion or so in cuts that the administration is planning -- just for starters -- in its 1983 budget will have to come out of state and local aid. The only hope on the horizon is the frequent rumor that the president wants to revive his old idea of returning some federal revenues to states to help them pay their new bills.

The governors, however, are unlikely to embrace this promise with the same naivete with which they once endorsed the administration's early budget plans. The first question is where will the money come from? The administration gave away a substantial part of the Treasury last summer, and revenue losses will grow as the delayed portions of the new tax law come into effect over the next few years. The president may weaken in his opposition to any tax increases, but the federal government is going to need all the money it can lay its hands on just to keep its own deficit out of the $100 billionplus range.

So it appears that any token transfer of revenues to the states will come tied to a much larger cut in federal aid. Some sweeteners in the form of further reductions in federal rules and regulations may be added to the package, but the governors are still likely to view this gift with a jaundiced eye. One cause for concern is the kind of taxes included in the deal. Tobacco and liquor taxes are frequently mentioned sources. The governors should ask themselves whether the revenues from these taxes are likely to keep pace with expanding needs -- such as health care and welfare -- that they will have to support.

Then there is the matter of distributing the money. The most common formulation is to add the earmarked tax revenues to general revenue sharing. That's not a good idea. At present, states don't get any revenue sharing at all.The old formula that distributed money to the states until last year could be revived. That formula, however, was so rigged to serve the interests of powerful congressmen, at the time that it was devised, that many of the hardest-pressed states benefited least from it.

As for the formula that delivers revenue sharing to localities, it is one of the atrocities of American federalism. It was revenue sharing -- not a special purpose federal grant -- that built the tennis courts that so infuriated David Stockman in his rural home town. It is also local revenue sharing that has led to the creation of thousands of useless "toy governments" created in every suburban and rural hamlet for the express purpose of receiving and spending this form of federal aid.

Presumably some better and fairer formula could be devised. But the present Congress has not shown any inclination to deal with the finer points of equity and efficiency. Revenue turnback may or may not be a good idea -- the details are important -- but it is not likely to be something that will slip easily into federal law.