The hard-earned lesson of the Cuban refugee phenomenon is that it cannot be resolved independent of Washington's immigration policy in general, or without regard for America's obligations to a multitude of refugees from other countries.

In an understandable but ill-advised burst of sympathy, President Carter welcomed the Cubans with "open arms" (constructed as a blanket invitation), but he has since discovered that he was not reflecting U.S. public opinion. The latest national polls show that Americans, by more than 3 to 1, regard the Cuban influx as "bad" for the country.

While that doesn't necessarily mean the public is indifferent to the plight of the Cubans, it does show that there is a widespread (and well-founded) feeling that a problem as vast and global as the disposition of refugees cannot be handled effectively on an emotional, ad hoc basis, as with Cuba.

More than 3,000 refugees a day have been pouring into Florida, with the total already exceeding 60,000. If they kept on coming at that rate, there would be a million within a year. Anything remotely like that would simply wreck the carefully drawn plans of Congress to deal with the overall refugee problem in an orderly, non-discriminatory way.

"The integrity of the immigration system itself is being threatened," warns an experienced congressional staff expert. "You've got 13 or 14 million refugees worldwide, out of which you've got to select a couple of hundred thousand for admission to the U.S."

The State Department reports that it gets four million visa applications a year from people who want to immigrate to the United States. The upshot is that there is a long wait, even in same preference categories. If, as seems to be the case, many of the Cubans are economic rather than political refugees, should they be accepted ahead of millions of others who have been waiting a long time to come to the United States through the normal immigration system?

In an effort to update the system, Congress recently passed the Refugee Act of 1980. Signed by Carter on March 17, it sets an annual limit of 270,000 on ordinary immigrants. It also authorizes admission of 50,000 refugees a year, although the president, after consultation with Congress, may raise the ceiling for "special humanitarian" reasons.

The new law establishes for the first time precise procedures for admitting and resettling refugees, but the rules have been largely ignored in the frenzied flood from Cuba, which caught the government by surprise. Apparently, the White House now intends to bypass the law (and consultation with Congress) by treating the Cubans as applicants for "asylum" rather than as refugees, but this will surely raise new questions on Capitol Hill.

Roger Conner, director of the Federation for American Immigration Reform, thinks the president should set a definite overall annual ceiling for all refugees. Then, he says, "if Carter wishes to admit more Cubans, he would have to admit fewer people from Southeast Asia, the Soviet Union, Mexico or whereever."

When Conner was asked if there is a special case for those Cuban refugees who want to be reunited with their families in the United States, his answer was: "If a Mexican-American rented a truck, drove to Mexico, picked up all his relatives and drove back across the border, we'd impound the vehicle and imprison him for smuggling. Try to explain to Mexican-Americans the difference between that and what the Cubans in Miami are doing."

It is said that the Cubans landing in Florida are "voting with their feet," but the same can be said of millions of other refugees around the world who also have been fleeing poverty and repression. There are six million to eight million illegal aliens in the United States, mostly impoverished Mexicans who literally voted with their feet when they slipped across the American border.

There are now over seven million U.S. citizens out of work, with 700,000 losing their jobs just last month. Hence, it is hardly surprising that the public does not welcome a chaotic avalanche of refugees. Nevertheless, Americans need not feel defensive about this, for we have accepted more immigrants and refugees this year than the rest of the free world combined.

Moreover, most Cubans, on balance, are better off than the would-be refugees in neighboring countries of the Caribbean and Central America, where poverty, disease, illiteracy, repression and internal strife are more extreme than in Castro's domain.

If our government is genuinely concerned with the welfare of the Cubans, it could quickly improve their standard of living by lifting the harsh trade embargo we have imposed on the island for almost 20 years. Although the embargo was aimed at Castro, the end result has been to punish not him, but his helpless constituents.

As Sen. George McGovern has pointed out, "It does not make sense for us to trade with the two biggest communist countries -- China and Russia -- while claiming it would be dangerous to trade with a tiny island such as Cuba."

Like many others, the senator wonders if the "current confusion over the flood of Cuban refugees" could not have been prevented if the United States had joined most of the other major powers in maintaining regular diplomatic and trade relations with Cuba.