FRESH IN office and fresh out of cash, the new mayor of Washington is swiftly and methodically touching every base in her quest for municipal solvency. This includes the toughest and perhaps most critical players in any such mission, members of Congress whose snapshot impressions of the District of Columbia can affect every federal dollar this city seeks. For those members of the House and Senate who may not have checked out the change of command at the District Building, we would cite a number of moves by Mayor Sharon Pratt Dixon as well as D.C. Council Chairman John Wilson that demonstrate a seriousness of purpose and a sophisticated recognition of the federal/capital city relationship at its best.

There is evidence for Congress that the District is determined to cut costs. The Dixon administration was barely a day old when the order went out for deep cuts by every agency. Office-by-office management reviews have begun, and certain jobs are already dropping off the flow charts. Pay raises that were in the offing are now out of the question. Furloughs and layoffs are possible. Last week in fact, the D.C. Council took an extraordinary step, unanimously approving Chairman Wilson's proposal to furlough each member of the council and all of its 172 employees for 10 days. Mr. Wilson won approval for a total reduction of 10 percent in the council's operating budget. This matches the cut that Mayor Dixon had asked the council to make. Mr. Wilson also has his own proposal for taxes and budget cuts.

That's commitment. It demonstrates that although the mayor and chairman may have their differences over policies, executive-legislative cooperation is working well.

In several low-key but telling ways, Mayor Dixon has sent signals to the Hill that the new city government understands some of the concerns of Congress about actions taken by the District -- even though ideally the city's elected government should be able to make local decisions without interference or financial punishment by those in Congress who still can control the city government's money supply. It is not a question of groveling and begging but of working to resolve congressional concerns without damaging the local interest or the limited self-government that the District worked long to win.

A reasonable example of this good spirit: Mayor Dixon and Chairman Wilson are taking a second look at a local bill that would make manufacturers and distributors of certain firearms legally liable for deaths and shootings involving weapons that they market. This measure, which still is subject to congressional review and possible rejection, has a national impact. If something can be worked out that 1) avoids a congressional rebuff of a local action and 2) eliminates possible opposition to more federal money for the District, that's a fair plus. Should Congress have this kind of control over D.C. legislation? No, but it does, and until that is changed, some meetings of the mind should occur without sacrifice of principles.

There will be occasions for standing up to Congress for those principles, and there's every reason to believe Mayor Dixon and Chairman Wilson would do so if they had to. But if the city government is respected in Congress and in the White House, the case for the federal government's fulfillment of its financial responsibilities can be made to a more receptive audience. The solvency of the capital city is at stake.