More than 3,000 Ethiopians are pouring into Sudan daily, overwhelming facilities that already hold more than a half million refugees from famine and drought and further burdening a country that faces the prospect of starvation for nearly one-fifth of its own population.

Despite a U.S.-led emergency famine relief operation, refugees still are dying of malnutrition, disease and lack of medicine. Even optimists among relief officials refuse to pronounce the situation under control.

At best, an American official said, with the caution shared by other relief workers, "we are trying to stabilize the situation. We've got 10 fingers in a dike with 14 holes."

Relief workers, especially among the younger men and women in the private voluntary agencies, blame the Sudanese government and the United Nations bureaucracy for failing to sound the alarm in time. Even two months ago the official word here was that Sudan was suffering from drought, not famine.

President Jafaar Nimeri waited until Dec. 31 to appeal for international help, although regional officials in the western part of the country had declared a state of emergency a year ago.

Sudanese officials protest that they could not have foreseen the vast numbers of refugees that would stream across the border, and western aid officials concede that Sudan has been generous in taking them in.

Inevitable logistics problems in a country one-third the size of the United States -- but one of the world's 25 poorest -- have created major difficulties for harried planners, who so far consistently have underestimated the extent of the problem nationwide.

Only last week, for example, all rations ran out at the major Wad Sharife camp for Ethiopian refugees, near the eastern city of Kassala and just off the main road leading to Port Sudan, entry point for relief supplies.

What one relief worker termed a "total cataclysm" was averted by local purchase of hoarded sorghum, the main staple here. But he said bitterly, "There never should have been such a sudden hiatus."

In addition, airlifted supplies and the dispatch of two grain-loaded ships to Port Sudan were designed to meet the challenge of the 3,000 refugees arriving from Ethiopia every day.

The food pipeline for those refugees -- who arrive on foot from Tigray Province in disciplined but physically weakened ranks -- should be "primed and disgorging" by the end of the first week of February, according to relief officials.

Admitting that the interruption in rations -- and the extreme malnutrition of about 20 percent of the children reaching the camps -- "might look like a disaster," one official said, "it is still one hell of a response in extremis."

By that he meant refugee organizations and relief organizations, especially the United Nations High Commissioner for Refugees and the Sudanese government, had been caught unprepared for the massive influx of refugees despite persistent warning signals and were slow in sounding the alarm for international aid.

"Yes, we are going to keep people alive in the short term," a relief specialist said, but he wondered what would happen in the long term to the depleted herds of cattle and other livestock whose carcasses litter the land.

It is estimated that 127,000 refugees have arrived from Ethiopia since the flow accelerated in October and that as many as 600,000 will have arrived by the end of March. The number of Ethiopian refugees here had been estimated at 450,000 before the current crisis.

Although most international attention has focused on the Eritreans and Tigrayans who fled from Ethiopia, relief workers are worried about the threat of famine to as many as 4.5 million of Sudan's 22 million citizens.

Based on a worst-case projection last winter, the United States has mounted a much praised and smoothly functioning relief operation for Northern Kordofan and Northern Darfur provinces in the west.

Since November, sorghum, a tropical grass grown for grain, syrup, fodder and pasture, has been shipped from Port Sudan as far as 850 miles into the interior, first by large truck, then rail, then in smaller trucks and distributed to 22 district centers.

The United States has committed 102,000 metric tons of sorghum and wheat, compared to only 89,000 tons from the rest of the world. A further request for 387,000 tons is under study in Washington.

Nonetheless, with the third consecutive bad harvest and fears of a fourth to come, barring sufficient rains this summer, the remaining cereal deficit is estimated at 908,000 metric tons, almost half a year's normal production.

"If you think things are bleak now," a relief official said, "you'd better start saying your prayers for next year." The next harvest is in November.

"If there is no more aid come April, May or June," a relief official said, "people on the geographic and financial fringes are going to hurt."

Moreover, relief officials now foresee the need to provide food for 1 million Sudanese in the eastern provinces, the traditional breadbasket that in good years exports cereals.

Last year's sorghum crop, although better than the virtually total failure in the subsistence farms of Northern Darfur and Northern Kordofan, was only 25 percent of the 1981 record harvest.

In addition, between 200,000 and 300,000 nomadic tribesmen from the Red Sea hills on the coast also are reported to be suffering from famine. And many supposedly settled Eritrean refugees who over the years have melted into the Sudanese population now are exercising their rights as refugees as food supplies run short in the east.

A relief official in Washington said Sudan also faces an influx of refugees from its western neighbor, Chad. He said that 90,000 nomads from tribes that are out of favor with the Chadian government and are not getting food rations had crossed into Sudan as of late December.

But the recently arrived refugees from Ethiopia present the greatest immediate danger. Many suffer from malaria, malnutrition, body lice, vitamin deficiency and ulcerated eyes. Relief officials fear possible epidemics of measles and meningitis.

Belgian relief doctors at Wad Sharife estimated recently that 20 percent of the children arriving at the camp were underweight to the point of being in danger of dying unless intensive nutrition and medical treatment was forthcoming.

A visitor to the camp last week reported that the refugees were forced to give up part of their meager rations and to pay for milling their grain and for water. There were no jerrycans or water tanks in evidence.

"We are living from day to day," a U.N. relief official acknowledged.

Hassan Attiya, Sudan's deputy commissioner for refugees, complained in an interview that Sudan was being unfairly attacked by foreign relief workers for being slow off the mark and failing to centralize relief efforts, as long has been the case in Ethiopia.

"We were not too late in sounding the alarm," he said. "But we simply did not expect such large numbers of refugees from Ethiopia."

Whatever Sudan's failing -- and the country is suffering from civil war and virtual economic collapse -- it nonetheless boasts an unblemished record for welcoming all refugees.

"That is something they are not given credit for," a U.S. relief official said. "When 30,000 Cubans arrived in Florida a few years back, you would have thought the U.S. was going to collapse. What's happening here is comparable to having 12 to 15 million Mexicans come across our border. We'd go nuts."