The Indian Health Service, a branch of the Health and Human Services Department that cares for native Americans, is facing a crisis--in funding, staff and morale--that many doctors say already is having an impact on the 800,000 Eskimos and Indians who are eligible for its free health care.

"We don't have the money to take care of everyone who needs it," a South Dakota doctor said. "Patients have to come in almost as emergencies to be treated. Luckily we're not following the orders from higher up. They just want us to treat people who are dying on the doorstep."

A common complaint is that because there are no nationwide standards as to how much Indian blood a person needs to qualify, many people are getting a free ride on the financially strapped program because of some distant Indian ancestor.

The tribes determine their qualifications for membership, and critics say some tribes want as many members as possible to boost their political power and get more federal dollars.

Since the early 1800s, when Army doctors tried to curb smallpox outbreaks in some tribes, the United States has provided some medical services to Indians. The IHS evolved from treaties in which the federal government promised to provide medical care.

The IHS now provides free treatment to Indians in federally recognized tribes who are not covered by other health insurance programs, including Medicare and Medicaid. It runs 52 hospitals and many more clinics around the country, ranging from 10-bed facilities in Northern Alaska to large buildings with 200 beds in cities like Phoenix.

What they have in common is a clientele who are frequently poor and relatively unhealthy. Indians, who often live in isolated reservations on infertile land, are more likely than the general population to suffer from pneumonia, strep throat, impetigo, alcoholism and ottitis medea, an inner ear inflammation.

While Indian health statistics look much better than they did when the IHS was formed in 1955, they remain below the average in America. In 1970, the last year for which the IHS has data, the life expectancy of Indians was 65.1 years, compared to 70.9 years for the overall U.S. population. In the late 1970s, infant mortality for Indians was 16.4 per thousand live births, compared to 14.1 for all Americans.

But at a time when health care costs are rising dramatically--15.1 percent in 1981 alone--the IHS budget has been trimmed from $626 million in fiscal 1981 to $600 million this year. The Reagan administration has proposed $613.2 million for fiscal 1983, which begins Oct. 1.

Joseph N. Exendine, deputy director of the IHS, said the agency has scrimped on travel and administrative allowances but has not had to cut back on services.

But doctors in the field who were interviewed disagreed, noting that they have been ordered not to contract for outside medical services except in emergencies. In many small hospitals, which lack surgical facilities and thus have to contract for almost all major services, the budget simply won't cover what must be done, doctors said.

For example, in the Cherokee area of Pahlequah, 70 miles southeast of Tulsa, $70,000 is available each month for contracted services for a hospital serving 45,000 people. That goes quickly--a coronary artery by-pass operation may cost $25,000 or more--so chronic problems often are not treated. Cataracts may not be repaired and expensive surgery to replace joints is not performed.

"Nobody's going to die. It's just going to hurt all the time," one doctor said. "It's quality of life."

The problem could get worse because of an impending shortage of doctors. The source for up to half the IHS physicians and dentists has been a scholarship program for medical students who agree to serve in the IHS for several years. The Reagan administration plans to phase out that scholarship over the next three years.

Many doctors resent having to treat people with only a tiny amount of Indian blood. Congress has avoided the sensitive issue of defining who is an Indian, so anyone registered by a tribe, and his or her spouse and children, can qualify for the free medical and dental care.

In some states, where Indians are isolated on reservations and there has been little intermarriage, that is not an issue. But in others, such as Oklahoma, intermarriage was widespread and a large portion of the population has at least a little Indian blood. In jockeying for political power and federal assistance, tribes often have signed up anyone with any amount of Indian blood.

"Everybody and his brother is part Indian around here, and if the government is going to give free medical care, why not take it?" one Oklahoma physician said.

That doctor, who works at a hospital in Pahlequah, said 40 percent of his patients have less than one-quarter Indian blood, adding that patients with just 1/128th or 1/256th Indian blood are not uncommon.

Dr. Charles D. Allen, clinical director of a hospital in Claremore, Okla., told of a patient who was less than one-thousandth Indian, and two other IHS doctors who asked not to be identified said they also knew of similar patients getting free health care.

Some IHS doctors object to having to treat these "blond, blue-eyed patients," and blame Congress for not restricting treatment. Others disagree. One Oklahoma doctor said it would be "pure unadulterated racism" to draw a line at some fraction of Indian heritage and allow people only on one side of the line to get free medical care.

Jake L. Whitecrow, executive director of the Denver-based National Indian Health Board, which acts as a watchdog over the IHS, said the decision about who is an Indian should be left to the tribes.

"Being an Indian is in your heart, how you feel," he said. ". . . It's being a citizen of an Indian tribe . . . . I know some who are 1/256th or 1/512th who are more Indian than those with full blood."