WHEN ALL the details of next year's budget cuts are finally worked out to the satisfaction of Congress and the administration, it will fall to the mayors and governors to figure out how to cope with the very large share of reductions which, directly or indirectly, affect their own budgets.

The District government is preparing for a triple whammy, since it combines the functions of state, county and municipality: cuts in federal aid in all those levels of government will fall directly on its budget. In addition, because Washington is a large urban area with a substantial low-income population, reduced help for cities and the poor will have a larger than average impact on the city's economy. And cutbacks in federal jobs and pay will also have a concentration effect on the metropolitan area.

Amidst the confusion of congressional action and the intricacies of the city's already tangled financial affairs, the District is doing the best it can to prepare for the worst. Tallies have been made of likely losses to each agency, and information is being collected from outside organizations that receive direct federal grants. Consultants have been hired to estimate the full impact of the new federal policy on the economy of the District and its close neighbors. Next steps will include translating money losses into reduced services and employment and, finally, trying to figure out how to soften these losses through some combination of improved management, reduced red tape and simple belt-tightening.

A first look at next year's expected loss in direct grants -- everything from day care, home care for the elderly and school lunches to urban development and highway construction -- puts the number somewhere between $60 and $80 million, the range depending on how harsh a cutback in federal Medicaid cost-sharing is enacted and how much local Medicaid costs can be cut. The estimate does not include this year's cut in revenue sharing or cuts in benefits like food stamps that are not counted in the District budget. Some offsetting savings might come from the Reagan proposals to consolidate special purpose programs into a few block grants, but Congress has been unreceptive to this idea thus far, and, even if the idea is accepted, it would take some time before adminstrative procedures could be streamlined.

While $80 million is not an overwhelming loss out of a $1.8 billion budget, it is only a first-round measure. Not included are the negative effect on local economic activity of the jobs lost directly or indirectly through the budget cuts and the reductions in local purchasing power that will come from cuts in welfare and food and housing subsidies. A smaller role for federal regulation generally may also dampen the interest of private industry in locating in the Washington area. All of this will reduce local revenues from income, business and sales taxes and put the District budget under further strain.

This prospect is especially uncheering coming, as it does, at a time when the District government is already finding it difficult to live within its means.With revenue sources already stretched, further cutbacks in jobs and services seem inevitable. That hard task is still to come. Nonetheless, for whatever comfort it may lend, the District government is at least starting on the right track in its planning for a tougher tomorrow.