IT REALLY doesn't matter whether Sen. Patrick Leahy (D-Vt.) or Rep. William Natcher (D-Ky.) or Mayor Walter Washington or the business community backed down, lost face or prevailed, as the case may be, in the convention-center battle. The important point is that the city's privations for lack of a 1978 budget are over. And the convention center, with all its promise of economic stimulus for downtown Washington, has been given a new lease on life. In other words, things are looking up for this community, after a drawn-out struggle between the chairmen of the House and Senate appropriations subcommittees, Rep. Natcher and Sen. Leahy, over just how much public money should be made available in the 1978 budget for the convention center. Mr. Leahy wanted the local business community to provide additional money to pay for the center, while Mr. Natcher championed the original proposal of the city officials and the business community. Now, after months of inaction, the chairmen of the subcommittees have reached a compromise not only on the center but also on about 20 other budget items. Their action, which is expected to be quickly approved by the full House and Senate, will allow the city to start spending money on new programs and projects that could not be financed under a continuing resolution that held spending to 1977 levels.

The newly approved budget dosen't give the city all that local officials requested.None of the money set aside for the University of the District of Columbia, for example, can be spent until the House and Senate subcommittees approve another master plan for that school. And federal payment, the money the federal government pays to the city instead of taxes, will be considerably less than city officials asked for. As for the convention center, the compromise that was agreed to still requires a substantial amount of work from city officials, the business community and the congressional committees. A totally revised plan for the center - subject to the approval of both appropriations subcommittees - must be drawn up before any money can be spent. That plan must include commitments from the business community to develop enough commerical activities throughout the city that additional taxes on those newly developed properties can cover the operating costs of the center - estimated to be about $8 million to $10 million each year. That money must be available three years after the center opens, which means that new commercial developments must be started quickly so that the tax money can begin to flow. The congressional compromise also requires city officials to come up with a less expensive proposal than the present $110 million estimate.

Where does that leave the city and the center? The mayor and city officials have started to meet with representatives of the business community to figure out a way to cut the cost of the center and to get some specific commitments for commerical activities around town. None of this is going to be easy. But the participants in those meetings are now talking about submitting a plan to Congress in short order, perhaps even within the next month or two. That's the spirit needed for the convention-center project - which seemed so close to extinction a few months ago - to become a reality.