MOST OF the city's hospitals are now providing millions of dollars' worth of desperately needed care every year to patients who can't pay. As a result most of these hospitals are sliding toward deep financial trouble. One of them, George Washington University's Medical Center, has gone to Congress for help. Its good friend, Sen. Daniel K. Inouye, an alumnus of the university's law school and a member of its board, is sponsoring an amendment to authorize a grant of $50 million.

The hospital's case is sufficiently urgent, and its services to the city sufficiently important, to make a compelling case for this grant. The money would have to be matched by the university, which would use it to renovate or replace a building that is now severely obsolete. Sen. Inouye's amendment is attached to legislation that is in conference and, let's hope, on the verge of passage.

The GWU Medical Center is now losing money at a rate of $25 million a year -- entirely because of uncompensated care to indigent patients -- and there's no hope of squeezing building funds out of the hospital's income. But while Congress certianly ought to provide this grant, this method of supporting care for the poor leaves a lot to be desired. It's uncertain, unreliable and potentially very unfair. A hospital of this one's stature ought not have to depend on influential friends at the Capitol. It ought not have to buttonhole members of Congress and remind them who it was that saved President Reagan after the shooting in 1981. Both Congress and, here in Washington, the D.C. Council need better ways of deciding where the need is greatest -- particularly for emergency care, which the Inouye amendment emphasizes. Emergency care is the main focus of the hospital's financial crisis, for the emergency room is the route through which most of the uninsured patients come in.

The city may very well lose two emergency rooms during the next year. Capitol Hill Hospital said earlier this month that it intends to convert itself to a long-term care facility, and Hadley Memorial Hospital in one of the city's poorest neighborhoods, Anacostia, may be forced by its deficits to close. That would throw an additional burden of unpaid care onto other nearby hospitals, with the predictable effect on their respective deficits.

The rising appeals for care from people who have no insurance are becoming a threat to every urban hospital in the country. Congress is ducking them, and the D.C. Council is ducking them. But where emergency rooms close because of uninsured patients, they will be closed for everybody.