IF THE STRIKE by musicians of the National Symphony Orchestra proves anything other than how painful and frustrating such situations are, it is that the long-run financial problems of this, and of other private arts organizations in Washington, are deadly serious. Without getting into who is right - or more right - in the immediate dispute, it is incontestable that without some steady level of funding, the symphony, the Washington Opera, the Corcoran Gallery of Art, the Folger Shakespeare Library and a variety of other institutions will almost certainly some day fold.

Unlike giant corporations, these institutions cannot meet the costs of inflation by raising prices. They could get their money from the federal government. But how? And why should they ?

Let's take the "why?" first. Why should private arts groups in the District be in a special boat in regard to public funds? The short answer is: because they already are. Ynlike an orchestra or museum in New York or Pittsburgh, they cannot turn to a state agency for money. They can't raise enough money from private sources because there are no private foundations of any size in Washington. And the big corporate donors, such as Exxon and Mobil, tend not to give to private arts organizations, but rather to the already rich federal institutions, where the fruits of their donations will get splashier show. Private groups have the recourse to choose to join up with a federal institution, as the Museum of African Art recently did with the Smithsonian. But that's limited option.

Technically, the District arts groups are in a position to get federal funds right now, though not for the things they need the most. Federal agencies such as the arts and humanities endowments are always happy to provide support for short-term projects.

But what the District arts groups need - indeed, what private cultural institutions throughout the country need - is money for heat, rent and salaries. Some of the more prestigious organizations, such as the symphony and the Folger, have recently banded together into the D.C. Consortium, and have asked the endowments to earmark special allocations for them. But the endowments are not intended to provide basic costs, and they are supposed to be open to free competition among would-be grantees.

A logical place for the arts groups to turn is the D.C. Commission on the Arts, but the commission is strictly a sub-granting arm of the arts endowment, and so must be held to the same strictures. What is needed, we think - and here's where we get to the "how?" - is a different approach.

If the arts groups in the city were to band together, not into a consortium made up only of the bigger organizations> but rather of all private arts groups - from the NSO to Jim Greggs's "Sign of the Times" gallery in Northeast - then they could operate as an amalgamation like the United Way. Just as the United Way sets up its own criteria for determining community need, so could the arts organizations. Then they could apply as a single, unified organization to the federal government for an amount each year - it would not take a great deal - and disperse the funds among the member organizations.

We don't swer by this particular solution, though we think it's worth a try. The point is, if we want to continue to have private arts organizations in this city, we must be prepared to pay part of their way. Otherwise, some of them will eventually exist only for the very rich, and others not at all.