Washington — Whatever President Reagan's ''new federalism'' may bring about in the future, many state governments right now have their hands out to Washington for more help to take care of the jobless.
Seventeen states, according to US Labor Department officials, now owe the federal government $6.72 billion in loans to pay the unemployed, and the total is rising.
This money comes from the so-called Federal Unemployment Account (FUA), lent by Washington interest-free to states that have run out of money to compensate their unemployed.
FUA in turn is asking Congress to appropriate an additional $1.1 billion to bolster the shrinking fund through March 31. After that, if unemployment remains high, the Reagan administration may have to ask legislators for more money.
Only last December Congress appropriated an extra $2.3 billion to replenish FUA coffers, as unemployment nationwide soared to the current 8.9 percent.
House Speaker Thomas P. O'Neill Jr. (D) of Massachusetts pledges swift congressional action to keep a pipeline of aid going to Americans who have lost their jobs.
Nothing better illustrates the havoc wrought on federal budgets than the kind of recession in which the US economy now is mired. Each 1 percent rise in unemployment translates into a $25 billion loss to the US Treasury. Fewer workers pay taxes and more jobless people need help.
An increase of only one-tenth of 1 percent in jobless totals, officials say, can add as many as 100,000 Americans to food stamp rolls.
Normally, FUA is supplied with money from a federal tax on the first $6,000 of an employee's income, paid by the employer. Only when the fund runs dangerously low - as now is the case - does the secretary of labor ask Congress for a special appropriation to bolster FUA.
All this supplements money raised by state governments through their own taxes levied on employers' payrolls, typically up to 9 percent on the first $6, 000 paid to each employee. In some states the taxable wage base is higher than $ 6,000.
The Reagan administration and Congress, through the Omnibus Budget Reconciliation Act of 1981, made it harder for jobless Americans to qualify for more than 26 weeks of unemployment compensation.
Thus, as the year moves on, more and more people laid off for longer than 26 weeks may have to go on welfare, when their jobless benefits run out.
All this frustrates White House officials, who - in their zeal to trim government spending - cut, or thought they had cut, both welfare and unemployment costs.
Until 1970, 26 weeks was the maximum duration of unemployment compensation. Then Congress passed a 13-week extension and later, during the 1974-75 recession , two more extensions, up to a total of 65 weeks.
State governments paid the basic 26 weeks (except when they had to borrow from FUA), state and federal regimes split the first 13-week extension, and the federal government took care of the second and third extensions.
The latter two expired, rolling the situation back to 26 weeks of benefits, plus an additional 13 weeks under limited circumstances.
The 13-week extension used to be triggered automatically, when unemployment nationwide reached a seasonally adjusted 4.5 percent level. The national trigger was abolished by last year's tightening of the law and state triggers were raised.
The cumulative effect of these changes, according to AFL-CIO social security director Bert Seidman, was to cut more than 600,000 long-term unemployed people out of the system.
In December 1981, to take the latest example, the Labor Department reported that 8.9 percent of the work force - roughly 9.5 million people - had no jobs.
Not all these people receive unemployment compensation. Some have run through their 26 weeks. Others are newcomers to the work force and had not, at the time they were laid off, accrued enough time to qualify.
In addition, said the Labor Department, another 1.2 million Americans are ''discouraged workers'' who have given up looking for jobs and no longer are included on unemployment rolls.
From all this a complex picture emerges. The government pumps billions of extra dollars into the compensation system, as unemployment climbs. Yet, because of tightened rules, many people find those benefits harder to get.