In the back of a tiny room in a storefront at 13th and N streets NW, two very different women sit, both waiting to see a doctor, both tired, not feeling very well, both black.

They are patients at the Zacchaeus Medical Clinic, a six-year-old operation which is believed to be the only source of completely free medical care for many Northwest D.C. residents. One of the women, a well-dressed typist, has been coming to Zacchaeus since it opened in 1974, not because she can't afford her own doctor, but "because they treat you like a human being here. The doctor always has time for you and the atmosphere is genuinely humane."

She does not live in the neighborhood, and has to drive to her appointments. She regularly makes a donation which she says she would be more than willing to increase "before looking for one of those idiots with a fancy office and no heart."

Beside her sits a large, friendly, sad-eyed woman whose MedicAlert necklace says "diabetic." She is a resident of a nearby shelter for women, and first came to Zacchaeus on a referral for a routine physical. Employed one day a week as a domestic, she says that she would have no place to go if the clinic closed, adding, "It would be the end of me. I just can't make it without my medicine [insulin], and there's no way I can afford to buy it myself."

But in spite of the high marks it earns from patients, the Zacchaeus Medical Clinic is in serious trouble and may close by the end of the summer if additional sources of funding are not found, said Marcella Donahue, one of the clinic's two full-time coordinators.

The clinic primarily serves residents of the neighboring community who cannot afford to seek medical care elsewhere. Between 5 and 10 percent of the patients are street people -- alcoholics, prostitutes and drug addicts -- from the nearby 14th Street corridor. For them and for others among the nearly 3,500 persons who were treated last year, the sharply rising costs of malpractice insurance, pharmaceuticals and utilities, along with the spiraling inflation rate, may spell the end of the privately funded clinic that is their basic health-care resource.

Originally opened under the auspices of Luther Place Metropolitan Church, the Zacchaeus clinic became independent in August 1977. Today it generates its own monies, mostly from small, individual contributors and a variety of church and charitable groups.

Financial problems began when it was realized that the cost of medicine would exceed the 12 to 15 percent increase planned for in the clinic's $39,270 operating budget for the 1979-80 fiscal year, Donahue said. Many of the people treated have hypertension, she noted, adding that the cost of medicine used to control it has nearly doubled. That type of budgetary strain, along with inflation and the increased patient load, accounts for the clinic's almost constant deficit operation, she explained.

"We were operating in the black once," Donahue said wryly. "In January we were ahead by $156."

They have remained open by dipping regularly into a $15,000 savings account built up during a period when malpractice insurance was not available to many free clinics in the area. When those funds run out, Donahue said, Zacchaeus will first try cutbacks, and then close. She, like others on the staff and steering committee, believes that it is important to continue offering all services without charge. It is not even suggested that patients who are in a position to do so make a donation, although there are some who do.

The four paid staff members receive subsistence salaries of $6,000 a year, and the doctors, pharmacists, technicians and others who complete the operation do so on a volunteer basis. Zacchaeus has made an emergency appeal to its donors for more money.

"If we have to cut back, malpractice insurance would be the first thing to go," Donahue said. "And that alone might close us down, because without insurance, you have a hard time getting volunteer doctors. Next, we would be unable to take any new patients, we might have to charge for medicine, and ultimately, we'd have to make some cutbacks in the paid staff, the number of sessions, the daytime clinic . . ."

Her voice trailed off as one of the volunteers came in to ask if they can treat a new patient that evening. The clinic has a limit of five new patients each night, "but it's so hard to turn someone away," Donahue said. The person in question is someone who has been having seizures and is reluctant to see a doctor. One of the volunteers had talked him into coming to Zacchaeus, and she was afraid that he wouldn't be back if he was sent home.

"Of course, of course," Donahue sighed, leaving the office area to talk with the prospective patient. There would be several others who could not be sent away before the long evening was over.

Clinic staffers believe that the increasing number of new patients may be due to the impending closing of the nearby Upshur Clinic at 1325 Upshur St. NW. That operation, which also serves many of the city's poor, is slated to shut down on May 20, a victim of the city's budgetary crisis. Donahue said that the Zacchaeus clinic had anticipated helping with some of the overflow, "but now," she said flatly, "we may not be able to do much good."

In the clean but crowded reception room, patients waited their turn. Most of them have no idea that the future of the clinic is in jeopardy, although the organization's board meetings are open to everyone. Many of these people live in the neighborhood, and come in for routine medical care. A fair number of them have diabetes or hypertension, and to a person they resent being "thought of as just a bunch of junkies hanging out near 14th Street and coming in for VD shots," as one woman put it.

For all of them, the prospect of losing the clinic is disturbing.

"I see other clinics closing, cutbacks everywhere, and it scares me," one woman said. "It's a real disaster for people like me. I think that [Mayor] Barry ought to take a real good look before places like this and Upshur are allowed to close down. This is badly needed. For a lot of people -- people like me -- it's the last hope."