THE REAGAN administration's chief budget strategist, OMB director-designate David Stockman, observes that only economic growth and inflation control can really reduce the federal budget deficit. But he has also noted the importance of linking stimulative tax cuts with a cut in federal spending deep enough to allay fears of inflationary pressure. Can he succeed in budget control where his predecessors have failed?

Budget cutting is not exactly a new preoccupation in this town. President Carter waged a three-year war with federal agencies and Congress to control federal spending. The battle was not complete in vain -- per capita non-defense spending has declined by about 3 1/2 percent in the last two years -- but the effort was thrown out of whack by an estimated $25 billion increase in spending this fiscal year caused by higher unemployment, prices and interest rates.

Mr. Stockman is aware of the practical necessity of early consultation with congressional leaders and interest groups -- a nicety too frequently ignored by the Carter administration. But such efforts at creating a consensus also require that budget cuts be fairly and broadly distributed. In a country this rich, the main burden of fighting inflation cannot be put on those least able to bear it: the poor and the unemployed.

A broad-based cut in benefits is essential in any case to provide enough money to support a healty tax cut. And a tax cut must be big enough to convince the many taxpayers who benefit directly from the government programs that they are not losing out on the deal. This suggests two other important principles: tax cuts should be linked to spending cuts, and the spending cuts should be presented as a package. No dessert without the spinach.

Some things, as a practical matter, can't be cut; air traffic controllers are the favorite example. But there aren't many others, and a few programs probably deserve outright annihilation. The idea of an across-the-board cut for most programs shouldn't be dismissed out of hand. True, it implies changing the terms of entitlement programs at least temporarily (one easy way is to defer cost-of-living adjustments briefly), but it avoids having to reorder priorities substantially, a difficult job to do in the rush of a first budget season. Some improvements might also be sought on the revenue side, such as withholding tax on interest and dividends, a big money-raiser with no effect on tax rates for the honest.

Finally, don't fool yourself. Shifting real costs from the federal budget to states and localities or to hospitals and businesses doesn't make them go away.

Getting the public and Congress to go along with a budget- and tax-cut strategy will require what the Carter administration didn't supply -- a strategy what is not only mindful of the gains and losses involved, but clear and coherant as well.