The great dilemma over the American cow, whose milk feeds a nation and clogs government warehouses, is beginning to take on new and awesome proportions.

Research here at Cornell University indicates that by 1990, the prodigious output of America's dairy herd can be increased dramatically, perhaps by 20 percent, by injecting a hormone developed through biotechnology.

The prospect of a new geyser of milk adds another perplexing layer to an already perplexing situation. A generous federal dairy support program, crafted largely by the dairy lobby, and other economic factors have led farmers to produce far more milk than the nation consumes. Buying and storing it cost the government more than $6.1 billion over the last three years.

The advent of the bovine growth hormone (bGH), as well as dozens of other advances in plant and animal science, puts an extra spin on the problems facing Congress and the executive branch this year as they rewrite basic farm legislation, including the dairy program.

New production gains in milk and grains, coming on the heels of surpluses that have pushed federal farm program costs to record highs during the Reagan years, have the potential to throw U.S. farm policy out of kilter and to create major new strains on the country's agricultural structure.

But they also offer the possibility of vastly increased production that could feed many more of the world's hungry.

So a major quandary results: How can U.S. farm policy be adapted to these fast-approaching and highly promising changes without creating additional upheaval in an already churning sector of the economy?

Some examples:

The long-heralded era of hybrid wheat has arrived, with a number of companies marketing limited supplies of the high-yield seed. But wheat already is a big surplus crop, and average yields are increasing steadily with traditional seed. The hybrids could mean an explosion of production and bring new pressures on government to absorb surplus crops.

* The same technology that brought hybrid wheat, according to the Agriculture Department, apparently can be used to hybridize barley, another grain supported by the federal farm program and a major ingredient in beer and American livestock feed.

* In some parts of the country, dairy farmers soon will be able to buy a new feed additive, developed by Eastman Kodak Co., that yields about 10 percent more milk and allows a reduction in the amount of feed given the cow.

* Work continues on a growth hormone that could help plants mature more quickly. Success would mean that crops could be grown in areas where the climate now is too hostile much of the year. In other areas, two crops a year instead of one would become reality.

* New purple-seeded varieties of wheat have been marketed recently by a California company as a high-nutrition alternative to the corn and soybeans typically fed livestock and poultry. Purple wheat reportedly yields up to 125 bushels an acre with irrigation. It also thrives in arid zones and could be an attractive crop for corn and wheat farmers in the Plains states, whose irrigation is fast depleting the midcontinental underground aquifer.

* Still other developments in wheat, combining better seed varieties and new planting techniques, indicate that Northeast farmers are on the threshold of 100-bushel-an-acre yields in an area that averages 30 bushels. Extensive testing shows that these higher yields are readily attainable by most farmers.

* The USDA says that other improved animal technologies indicate "faster growth rates, less feed use per unit of output, increased disease resistance and more offspring per animal." These developments will affect farm and ranch operating costs, the need to grow additional grains and the availability of red meat in a nation where per-capita consumption has declined over the past decade. A Threatening Hormone

These and dozens of other similar scientific developments in agriculture -- particularly the use of genetic technology to create bigger and better livestock -- have raised difficult health, social, moral and environmental questions. But critics notwithstanding, science marches on.

None of these developments seems quite so immediate and threatening, at least to farmers and to the federal dairy support program that has governed the industry for 35 years, as the bovine growth hormone. Unlike other developments such as the hybrid seed, bGH has the potential for almost immediate impact.

Questions remain about commercial production and federal approval of bGH. But tests here suggest that it could increase U.S. dairy production about 20 percent nearly overnight. In the carefully managed Cornell dairy research herd, the top increases are pushing 40 percent.

The best-managed commercial herds, in the view of the Cornell experts, will profit the most from bGH. That is another way of saying that farmers who are poor managers or heavily in debt could be overwhelmed by more efficient competitors.

If, as some research indicates, feed rations must be increased as the hormone is used, then farmers in high production-cost areas such as the Northeast, which imports much of its feed-grain from outside the region, would be at a competitive disadvantage.

If cow-feeding rations will require more grains, then the advantage would go to farmers in regions where the land is more productive and gives higher grain yields. Western New York, for instance, would have an edge over Vermont and New Hampshire. 'Scary' Scenario

As Dale Bauman continues his bGH studies at Cornell, university agricultural economists are taking an unusual before-the-fact look at the possible impact of the hormone on American dairying.

Robert J. Kalter, the economist who heads the project, said bGH carries serious implications for the dairy industry as well as the makers of farm policy.

Kalter said New York dairy farmers surveyed by Cornell indicated that they would adopt the hormone quickly even if they had to inject it into each cow every day. "The farmers that remain after three years will have an 80 percent or higher adoption rate," Kalter said.

"If adoption comes as quickly as we think it will," added Andrew Novakovic, assistant professor of dairy marketing, "there could be a sharp impact on the industry. Some people will go out of business -- the high-debt farmer, the poor manager.

"What would happen to national markets? Prices would have to come down . . . and come down substantially. A lot of other factors would come into play. But there are scary scenarios at the extremes. If the government maintains a price-support program with flexibility, I can conceive of an orderly situation in which fewer people get hurt."

Novakovic's "scary" scenario is one of the reasons for the Kalter study.

"There is a growing awareness that we need to think about this on the policy level," Kalter said. "Nobody has really come to grips with what to do next . . . This is not a marketing study that we're doing. It is an attempt to alert the public and the policy makers."

Another Cornell professor, rural sociologist Frederick H. Buttel, added: "There's not much disagreement on the facts. Under the present federal dairy program, with higher production, there would be a fantastically high cost to the taxpayer. One would expect bGH to put smaller farmers out of business . . . . The poorly managed small farms and the farms heaviest in debt would be most vulnerable.

"This will be the first major biotechnological impact on agriculture, but it won't be as great as the hybrid wheat, rice and corn improvements that are sure to come . . . ," Buttel said.

"[An irony] is that farmers who use technological advances do not benefit from them. Technological change tends to be production-enhancing, putting downward pressures on prices. And abnormal profits are bid back into a farmer's assets, so he doesn't reap the full benefits of technology." Widespread Use Foreseen

Although bGH seems so near as a commercial reality, word of its potential is just beginning to filter out.

"I've had calls in recent days about the bGH reports," said George Dunsmore, Vermont's former agriculture commissioner. "It is worrying people because of the huge surplus in the United States and because of the need to form a program that deals with it. But I don't think it has been talked about long enough to have much effect on the 1985 farm bill."

The experts here at Cornell see bGH becoming a commercial reality in widespread use within several years. But Monsanto Co., which is financing the research here and at other universities, conservatively estimates that its product may not be available until 1990.

Monsanto's David Crosson, in St. Louis, said that bGH faces a number of hurdles before it can be marketed.

"We have to test it in more real-life situations," he said, "and we don't think that daily injections as bGH now is applied are commercially feasible for the farmer. We're looking at some kind of longer-term controlled release. And even then, the product will have to go through approval processes of the Food and Drug Administration and its European counterparts."

Whatever the case, give or take a couple years, the portent for the federal dairy program seems large and dark. Even the more conservative agricultural experts, such as University of Vermont economist Fred C. Webster, see an impact coming.

"You have to make some heroic assumptions," Webster said, "but if bGH offers a good return, a lot of farmers would adopt it rather quickly -- more so than they have adopted artificial insemination . . . . I agree the potential is there, but style of management will be a key factor. I think there will be a real bump up in production."

Next: A harvest of tax breaks