Washington — After more than 300 years of virtually uninterrupted immigration, the United States still is having trouble coping with fresh waves of newcomers. Being "a nation of immigrants," as Americans sometimes proudly call themselves, often appears to have resulted in little useful expertise at dealing with immigration.
The country that has assimilated hundreds of thousands of black Africans, Irish, Italians, Jews, Germans, Scandinavians, Poles, and others finds itself struggling to absorb more recent influxes of Mexicans, Cubans, and Haitians.
So continually vexing is the immigration issue that it is despairingly described in Congress -- itself a microcosm of the US ethnic melting pot -- as "chaos," "out of control."
Current stresses and strains include:
* Cuban refugees. What to do about the sealift of Cubans that poured into south Florida, exceeding 110,000 in the past two months, plainly divides both the Carter administration and Congress.
The President, after initially welcoming the Cubans with "an open heart and open arms," later ordered the seizure of boats bringing them here. A presidential recommendation on financing the influx has been awaited for two weeks.
Congress appears receptive to shouldering much of the cost of resettling the Cubans. Lawmakers set aside $300 million in the current federal budget for Cubans (and Haitians), and the House of Representatives last week kicked in an additional $100 million.
But Capitol Hill seems reluctant to enact special legislation for them out of concern that it might uncork a new tide of Cubans.
* Calls for mass expulsions. Demands for wholesale deportation of aliens once again echo through the Capitol.
Last year, the target was Iranian students here who vocally supported the ouster of the American-backed Shah. More recently, their deportation again was called for after militants in Iran seized the US Embassy in Tehran, taking 53 American hostages. Now it is Cuban refugees who rioted earlier this month at a processing center at Ft. Chaffee, Ark., whose deportation is sought.
House majority leader Jim Wright (D) of Texas led the charge by angrily recommending that they "be given a one-way ticket forthwith and placed upon the very first aircraft or boat back to Cuba."
* Refugee law revisions. The embattled federal statute governing refugees was overhauled by Congress only last year, but already finds itself under new pressures.
Some administration officials and lawmakers now say the law, in effect less than three months, needs reworking.
"There is no doubt in my mind," says Rep. Carlos J. Moorhead (R) of California, a member of the committee that wrote it, "that the Refugee Act of 1980 must be reopened and perfected."
* Proposed new limits on immigration. Support appears to be growing in Congress for clamping a hard-and-fast limit on the number of foreigners allowed to settle here each year.
The new refugee law permits a "normal flow" of 320,000, plus an unlimited number under emergency circumstances. Legislation being pushed by Sen. Walter D. Huddleston (D) of Kentucky would impose an annual ceiling on immigrants from all sources -- 650,000 for this year.
* "Abscam" roots. The legislative cottage industry of cranking out private bills on behalf of individual would-be immigrants has bred corruption on the Hill for generations.
The latest is the implicating of six lawmakers in an Federal Bureau of Investigation "sting" operation for allegedly having accepted, or agreed to accept, bribes of up to $50,000 for introducing such bills to help a mythical Arab sheikh immigrate to the United States. So far two of them have been formally indicted.
* Opposition to illegal aliens. The steady stream of newcomers, chiefly from Mexico and other parts of Latin America, who elude the immigration machinery altogether -- estimated to number in the millions -- stirs continual resistance.
Moreover, the US Immigration and Naturalization Service itself has been without a permanent commissioner since Leonel J. Castillo resigned last October. The agency also has been subjected to allegations of corruption, mismanagement, and brutality in its dealings with illegal aliens.