Last week it became official: The nation is now formally in its seventh postwar recession, and by most forecasts it won't be the "short and mild" slump that the White House predicted only a few weeks ago.

Friday's grim report on unemployment, showing the jobless rate spurting in May to 7.8 percent of the work force from only 6.2 percent two months ago, marked the most dramatic evidence yet of the seriousness of the current slide.

And most other key inidicators recently have told a similiar story: Output is plunging, and preiminary indications suggest the current quarter's dive will be the steepest in postwar history. Moreover, there's no relief in sight.

But how bad will the current recession actually be? And what kind of recovery seems in store once the downslide is ended?

The Carter administration, clearly concerned about the economic issue in the current presidntial campaign, has begun trying to make the case that while the slump is certain to be steep, it may not last all that long.

President Carter told a campaign audience a few days ago that the nation now is "turning the economic tide." And Treasury Sceretary G. William Miller assured a congressional committee that the worst of the slump is over.

Both have firmly avoided any suggestion to propose a tax cut at least until sometime next year.

However, while such bursts of optimism have drawn their shre of smirks in the face of the current state of bad news, the administration isn't entirely alone in believing that the outlook may be somewhat improved now.

A small, but growing body of economists is beginning to believe that the recent dramatic plunge in interest rates, combined with the already apparent slowing of inflation, may help turn the economy around sooner.

"the chances of that are very good," says George L. Perry, a Brookings Institution economist who is wiely respected as an economic forecaster. "We could be recovering by early 1981."

Allen sinai, a Data Resources Inc. economist, agrees. The abrupt easing of the recent credit crunch, he says, is apt to bring "a quicker end to the recession . . . much earlier than if the crunch hadn't been reversed so quickly."

The rationale for this more optimistic outlook is simple enough:

Although the economy already was heading into a slump before last January's spurt in interest rates, most analysts agree that it was the sudden tightening of credit that ultimately pushed it so precipitously over the cliff. t

Last January's turmoil in the bond market -- and the abrupt surge in interest rates to a record prime rate of 20 per cent by April -- crimped business activity across the nation and sent the housing industry into a serious slide.

At the same time, the dramatic worsening of inflation last winter -- and the impositon of credit controls by the Federal Reserve last March 15 -- stunningly reversed consumber psychology. The spending spree ended. Americans retrenched.

In recent weeks, however, there's been visible relief, both on the price front and in interest rates. The prime rate has plunged to 13 percent. Mortage money is available again. And wholesale prices have slowed sharply.

The optimists argue that just as the recession was accelerated sharply by the sudden run-up in inflation and interest rates, so the decline will be softened somewhat now by the abrupt easing in financial conditions.

And they contend that a second major contributor to the slump -- the inability of the nation's automakers to produce enough of the small cars the American market now demands -- also should begin to turn around next year. t

Administration economists offer this scenario:

The housing industry, given a transfusion by lower home mortage rates and renewed availability of credit, will begin to revive as early as late summer.

Although housing starts has been slowing somewhat before March, the White House argues it was primarily financial factors that made the housing market collapse, and that buyers will come back now that these restraints are gone.

Unlike previous housing slumps, this time the collapse was so abrupt and brief that there are no massive unsold inventories for the industry to work off. Sales of existing homes already have picked up in recent weeks.

The nation's major automakers will finish their retooling for smaller cars early next year and should start producing more vehicles that meet demands for more fuel efficiency -- and hence will sell in the American market.

Even if the conversion is delayed, the optimists argue that at least auto sales won't be plummeting, as they have been so far this year. That factor alone ought to mitigate the downward drag on the economy.

Although consumer pyschology clearly has been reversed from the pre-March period, the more optimistic forecasters believe Americans will open their pocketbooks more one they see inflation coming down.

The Labor Department reported on Friday that prices charged by producers rose at only 3.7 percent annual rate in May, following a 6.2 percent pace in April -- well below the 18.2 percent annual rate recorded in February and March.

And economists expect the consumer price index to slow to a 10 percent rate between now and late autumn -- still high by historical standards, but well below the 18 percent pace that frightened consumers so much last winter.

Although some businesses already have trimmed back their capital spending, the cutbacks so far have been limited to short-range purchases, such as trucks. tMost longer-term investment projects are still on the books.

As a result, capital outlays are likely to continue moderately strong the rest of this year and well into 1981, maintaining significant momentum in the economy. A serious falloff would have ensured a long recession.

The Fed's monetary policy is not likely to remain as restrictive, if only because the central bank already has outstripped its money-reining targets and has no need to keep pulling back in the face of a declining economy.

Key Fed officials have indicated the board is now trying to speed up money supply growth to return to the upper range of its targets. Though most analysts belive monetary policy will remain unchanged, the threat of a crunch is past.

What all that adds up to, in the minds of those predicting this more optimistic scenario, is that the recession probably will end early in 1981 and the economy will begin recovering next spring, rather than continuing to be stagnant.

To be sure, at least some of these arguments seem reasonable enough. Most analysts agree, for example, that if interest rates do not surge again to their April levels, the housing market will bounce back quickly. And capital spending may remain relatively intact.

But most mainstream economist continue to be far more pessimistic about the third key element in the optimist's scenario -- the prospect of a visible pickup in consumer spending.

F. Thomas Juster, director of the University of Michigan's respected Survey Research Center, says the past few months' turmoil has reversed consumers' "buy-now" philosophy -- and probably for some time, to boot.

"Once having wrung that thing out, it's going to be very hard to snap back," Juster says. "I'd be very much surprised if any of this had much impact on consumer behavior generally."

And Otto Eckstein, president of Data Resources Inc., the economic consulting firm, notes that even if consumers' willingness to spend picks up, there'd be little likelihood they'd do it because they wouldn't have the money.

Unlike 1979, when consumers managed to offset a decline in real income by borrowing and dipping into savings, this year, Eckstein says, there are no such opportunities.

Not only is inflation seriously eroding consumer purchasing power, but workers will be hit with a massive $57 billion tax-hike in 1981 -- far more than could be offset by even the most generous post-election income-tax cut.

The figure includes $17 billion in higher Social Security payroll taxes beginning next Jan. 1, $25 billion in increased energy costs and $15 billion from inflation pushing taxpayers into higher income-tax brackets.

Finally, Harvard University economist Martin Feldstein questions whether even capital spending will remain as strong this year and next as the optimist say -- largely because of tax considerations.

Although Feldstein agrees the recent drop in interest rates may help here, he warns that many businesses will put off many major expansions until Congress enacts a speedup in depreciation writeoffs -- which may well not come until 1981.

Rather, most forecasters, Eckstein and Feldstein included, still foresee an "L-shaped" recession for this year and next in which the economy first plummets sharply and then simply languishes for several quarters.

Barry P. Bosworth, the former Carter administration inflation-fighter now a Brookings Institution economist, agrees.

"When you look at the situation, it's clear the private sector isn't going to generate its own recovery," Bosworth says, "and it's not possible for the Fed or the administration to act without refueling inflationary psychology."

In the end, economists concede it still isn't clear precisely how bad the downturn will be this time: The administration still could be proved right, or the slump could be the most severe since the 1930s.

In any case, however, analysts agree that even if the recovery comes early, the jobless rate still is likely to be in the 8.5 to 9 percent range well past the November election and into 1981.

President Carter may be correct in contending that the economic tide already has turned. But the consensus still is that the benefits won't be visible in any case for many more months to come.