One of every five American workers was unemployed at some time during 1981, the Labor Department reported yesterday, bringing the total to 23.4 million workers, 2 million more than in the previous year.

Nearly 3 million were unemployed for the entire year, the department said, including in that total only those who were seeking work actively. Workers so discouraged that they didn't even look for a job are not counted as unemployed.

The report came as Congress girded for a fight over a proposed $12 billion tax increase over the next five years to help support the foundering federal-state unemployment insurance system.

With the blessings of the Reagan administration, the tax increases were approved by both the Senate Finance and House Ways and Means committees as a way of strengthening the state unemployment insurance funds. Many are in such trouble that they can meet payments to jobless workers only by massive loans from the federal government.

As of June 30, 19 jurisdictions, including the District of Columbia, owed the United States a total of $7.7 billion as a result of these loans or earlier borrowings which are still not paid back.

A business coalition led by the Chamber of Commerce is opposing the tax increases and is seeking to have them rooted out of both bills, with the first test vote likely today in the Senate.

"We hope we have the votes to strike it from the bill," a chamber spokesman said.

The federal-state unemployment insurance system was created by Congress as part of the Social Security Act of 1935. It is a complicated hybrid. The states, within certain very broad federal guidelines, set their own eligibility rules and benefit levels, which vary widely, and finance them by an unemployment tax, averaging about 2.6 percent nationwide, levied on businesses.

There is also a federal unemployment tax paid by businesses, at present 7/10ths of 1 percent on the first $6,000 of each covered worker's salary. The proceeds of the federal tax are used partly to pay for certain special benefits and partly for grants to cover state administrative costs and for state units of the U.S. Employment Service.

The United States, by use of certain tax provisions, has the power, in effect, to force the states to raise their taxes and to alter their program rules.

The tax proposal before Congress would, essentially, raise the minimum amount of wages on which both federal and state unemployment taxes must be paid by businesses from $6,000 to $7,000, raise the federal tax rate from 0.7 to 0.8 percent and force the states to raise certain rates too.

This would yield $12 billion for the Treasury and the states over the next five years, according to figures used by the Ways and Means Committee.

Business groups, however, say the extra funds aren't desperately needed in many states and shouldn't be forced on them. States that need the extra money are free to impose extra taxes if they wish, they say. They contend that part of the impact of the federal tax changes would be to use money obtained in no-problem states to pay for costs elsewhere.

Impetus for the tax proposal came from the gradual worsening in recent years of the solvency of the funds in many jurisdictions. The system initially was well funded, but in the past several decades many states have failed to put enough money into their funds during good years to meet the demands of recession years when unemployment jumps. This situation is aggravated by the fact that recent recessions have had higher unemployment rates and have lasted longer than had been anticipated.

As a result, many states have run out of money during recessions to pay for the basic 26 weeks of benefits or for their share of an added 13 weeks available in high-unemployment states for workers exhausting their initial 26 weeks. The state pays half for this added 13 weeks, the United States the other half.

Even before the current recession started, some big industrial states owed huge amounts to the federal government left over from loans made during the mid-1970s recession.

The current recession is having a particularly sharp impact. About 4 million people are now on the benefit rolls, compared with about 2.5 million a year ago. Benefit outlays for the regular 26 weeks plus the extra 13 are expected to reach about $23 billion in fiscal 1982, a record.

So far in 1982 11 jurisdictions have had to take out loans from the federal government, and another eight, including the District, still owe from previous loans.

Michigan, Illinois and Pennsylvania each owed $1.6 billion, Ohio $1.1 billion, New Jersey $525 million, Connecticut $272 million, Minnesota $210 million and various others smaller amounts. The District's debt as of June 30, according to department figures, was $41.7 million.