Congress last week agreed on a George Aiken-like solution to delivering on its longstanding balanced-budget promise in the face of a fast-deepening recession: It declared early victory and prepared to get out.

Drawing on the former Vermont senator's Vietnam strategy, the lawmakers approved a fiscal 1981 budget plan that is nominally free of deficit -- enabling them to tell voters they've balanced the budget for the first time in 12 years.

However, as both congressional and administration experts have now conceded, Congress has made some serious spending cuts, the onset of the recession all but guarantees that the budget ultimately will end up in a sizable deficit.

The major question is: will both sides now continue economic policy on its present course or use "victory" as a device to abandon their fiscal austerity image and enact a major tax cut late this year or early in 1981?

President Carter has indicated he will resist any major tax-cut proposal as long as is politically practicable -- given the possibility that the economy actually may stop sliding soon and that antirecession action may prove unnecessary.

But if the recession continues to worsen as the majority of economists still are forecasting and the administration and the lawmakers begin to get edgy about the pocketbook issue, the situation could change abruptly.

In a sense, despite the symbolic victory declaration last week, both Carter and Congress are caught between a rock and a hard place on the balanced-budget promise.

The pledge was valid enough back when they proffered it, but neither side really counted on a recession this steep. With the slump now in force, the same austere budget that showed up balanced under January's forecast is clearly headed for a deficit now.

Budget experts now estimate that because of lower tax revenues and higher unemployment payments from the recession, updated estimates of last week's budget will show a deficit for fiscal 1981 ranging between $20 billion and $30 billion.

If Congress were to enact a major tax cut, that would boost the size of the deficit to somewhere between $45 billion and $60 billion -- a far cry from the modest surplus the president and the lawmakers promised in March.

The newly approved budget plan is only an initial target, based on last January's economic forecast. By law, the two houses must vote on a second budget resolution early in September, presumably based on a worsened economic outlook.

As a result, last week's vote on the initial budget resolution may in reality be the closest Congress gets to delivering a "balanced budget" for at least several more years.

Budget experts agree it's all but impossible for the lawmakers to stick to their balanced-budget pledge when the September measure comes up. Trying to eliminate the deficit by cutting another $20 billion in government spending would only make the recession far worse.

At the same time, both Carter and Congress have made such an issue about promising a balanced budget that it is going to be politically difficult to abandon abruptly even after last week's "victory" declaration.

The question is: will the obvious impossibility of adhering to the balanced-budget pledge provide a jumping-off point for both sides to embark on a major tax cut? And that answer still isn't clear.

Barely a few weeks ago, both the White House and Congress were still resisting a tax-cut bill this year, contending there still was substantial pressure for balancing the budget -- and relatively little for slashing taxes.

There also was the issue of how to counter Republican presidential candidate Ronald Reagan, who is calling for an immediate 30 percent across-the-board tax cut as the centerpiece of his economic program.

Carter aides reasoned the best way for the president to counter Reagan would be to take the conservative tack so he could paint the Californian's proposal as "irresponsible." And that meant resisting a tax cut for now.

But that was before the latest spurt in the nation's unemployment rate -- to an unexpectedly high 7.8 percent of the work force, from just over 6 percent two months before.

Most analysts now believe that if the jobless rise tapers off soon, both the White House and Congress can hold off on a tax cut until next January. But if unemployment continues to surge, voter reaction could turn around.

As of now, the situation is somewhat academic because in either case both sides are talking about a tax cut that would take effect next January, not in 1980. Carter consistently has avoided a 1980 tax cut as too inflationary.

Moreover, the administration has been wary about proposing another big policy reversal this soon after Carter's embarrassing March 14 budgetary turnabout.

Although analysts say Wall Street already has discounted the prospect of a near-term tax cut, it is still far from certain how the financial markets would react if he proposed one this early in the game.

As it stands now, Treasury Department tax planners are sprucing up their handiwork on a series of standard contingency packages -- this time most involving a cut in Social Security taxes and faster depreciation for business.

Virtually all sides agree that when a new stimulus package finally is enacted, it is likely to be almost entirely in the form of tax cuts. Both the White House and Congress are cool to the notion of boosting spending on the jobs program -- on grounds that they tend to be more inflationary.

But as of last week, the administration's top policymakers still were not formally considering such measures. And Carter was refusing to commit himself to a tax cut. Aides say he would rather hold out if possible.

Indeed, House Budget Committee chairman Robert N. Giaimo (D-Conn.) mused after last week's vote that budget-balancing fever still was so strong in Congress that even with unemployment soaring, "I honestly don't believe you'll be able to pass a budget with a $20 billion deficit" in September.

Giaimo said the budget-paring pressure from voters is so fervent that he believes many Americans will demand that their congressmen insist on keeping the budget deficit-free even if it means cutting another $20 billion in the second budget resolution.

That's the political horror that's facing the Democratic Party this year," Giaimo says. "Although we all here know you can't cut much further in recession, there's a basic judgment back there in the districts that you really could do that."

The budget fracas isn't the only economic policy setback the White House has suffered at the hands of Congress recently. The president's March 14 anti-inflation package also is in disarray.

Although the administration went to great pains to include Congress in the planning for the package, several of the program's most important elements are in deep trouble on Capitol Hill and others have been rejected entirely:

The $4.62-a-barrel oil import fee that the president imposed has been overridden by overwhelming majorities in both houses -- even though it was only at the lawmakers' request that Carter proposed the fee at all.

Carter's request to triple the administration's monitoring of price increases has been roundly rejected by the Senate and in the House Banking Committee -- with the program leaving Carter virtually without enforcement authority.

The Senate has voted flatly to repeal by mid-1981 the president's authority to impose credit controls, as he did in the March 14 package. Although the action won't affect today's controls, it's a clear slap at Carter.

The spate of new revenue-raising measures Carter proposed to help hold the deficit down -- a stepped-up cash management program, withholding taxes on interest and dividends -- is in serious trouble in Congress' tax-writing panels.

Even apart from the issue of balance, the fiscal 1981 budget the lawmakers approved is quite different from what the president and congressional negotiators had agreed on in March. Defense spending is much higher, for one thing.

Congress' reneging on the oil-import fee was seen by many observers as merely a flailing by the lawmakers to show constituents they were "doing something" for them. Key legislators report little actual pressure from constituents to vote the fee down.

The rest of Congress' backsliding was viewed as primarily a failure by the House and Senate leadership to exercise the necessary discipline to deliver on their earlier promises to administration negotiators. "Congress basically let them down," one participant in the negotiations says.

Speculation by some outsiders has been that Carter's next policy turn-about could come as early as mid-July, when the administration is required by law to update its economic forecast and budget estimates. But officials say the decision could well be postponed until later in the summer or early fall.

Carter already has backed away from his balanced-budget stance a bit, saying he now will insist only that the budget "restrain" the growth of spending, rather than fully eliminate any deficit, before he will consider a tax cut.

The administration's cabinet-level Economic Policy Group even has prepared a briefing paper with possible questions and answers for high-and middle-level officials. The document basically asserts that policy now is working effectively and no new tax-cut action -- or added spending on jobs programs -- is needed.

Meanwhile, both congressional leaders and administration policy-makers are conspicuously keeping their options open, ready to go either way once it becomes clear which way the voters want them to go.

The ultimate caution came from Treasury Secretary G. William Miller. Miller told reporters in a New York press conference: "Any reading of the president's remarks about a tax cut this year is a misreading of his position."