Will the Federal Reserve Board's latest round of credit-tightening really work? Or is the nation now headed into an unavoidable deep recession?

Those questions were on the minds of many Americans in the wake of the Fed's dramatic new moves last weekend to boost interest rates and tighten credit throughout the economy. And the answer depended, almost as much as anything, on the behavior of Jimmy Carter.

Although the president didn't ask for the latest round of credit-tightening by the quasiautonomous Fed, economists say Carter may now have more to do with the outcome of the central bank's actions than the man who initiated the new interest-rate plan, board Chairman Paul A. Volcker.

If the president can "hang tough" long enough for the Fed's harsh medicine to work -- as Carter said he'd on do Monday -- then the move could help cool speculative fever and dampen inflation. but if Carter hints he may try to counter the Fed action, he could blow the whole effort apart.

The administration's actions now are crucial because, in a way, what the central bank did last weekend was a loaded-gun scare tactic -- intended to nick the speculative bubble in the economy without seriously shooting holes in the underying level of real economic activity.

Besides raising its key discount rate from 11 percent to a record 12 percent, the central bank revised its entire approach to managing money and credit to place more emphasis on limiting bank reserves and less on interest-rate targets, and it increased reserve requirements for banks.

Experts agreed the dramatic action was necessarh to help dampen excessive borrowing that had fueled speculation in the commodity and exchange markets and to rein in the money supply, which also was growing far too rapidly. This combination of factors had sent the dollar into another slide.

Volcker told a television interviewer last week that the Fed was interested only in "limiting excesses." He promised that the board still would allow "moderate growth" in the supply of credit: "There will be enough credit to finance . . . orderly business expansion."

The key is that although the Fed's actions last weekend no doubt will intensify the recession somewhat, precisely how much deeper the slump will be depends largely on how long the central bank maintains its credit squeeze. And that, in turn, depends on how soon the speculative fever cools.

Many analysts contend that if the Fed's tactics work, the recession may be somewhat deeper than expected previously, but it also could wind up shorter. Inventories would be pared back -- and prove less of an obstacle to an early recovery. Money growth would subside. And speculation would abate.

But if the impact of last weekend's moves is vitiated, and the fever continues -- as seemed possible last week -- then the Fed would have to resort to even harsher and longer-lasting remedies. In that case, the recession could prove severe indeed.

As a result, both liberal and conservative analysts agree it is critical now that the nation believe the current tight-money policy is going to be pursued as long as is necessary -- and that means a united front by both the Fed and the administration, with the White House taking care not to undercut the board.

It was just this sort of logic that led to the orchestrated effort by the White House early on to support the Fed's credit-tightening moves -- sending a signal to the skeptical financial markets that Carter intended to go along with the Fed's actions and not to try to counter them with an easier fiscal stance.

Beginning last Monday, a spate of top Carter economic advisers led by Treasury Secretary G. William Miller, took to the hustings to endorse the Fed's action as needed and to reassert the administration's intention to keep fiscal policy tight despite the increased threat of a recession.

Budget Director James T. McIntyre even called for a near-blanaced budget.

But the hand-tought posture is bound to get more difficult in the coming weeks as the credit-tightening begins to take hold and major sectors of the economy start to suffer from the squeeze -- a development that many analysts are predicting may come quickly in the wake of last weekend's action.

Moreover, Carter is facing the added burden of having to endorse high interest rates at the start of a presidential election campaign -- virtually unprecedented in American politics. Sen. Edward M. Kennedy (D-Mass.), his chief potential primary rival, hasn't commented on the Fed moves.

Carter slipped once. After squarely endorsing the Fed move on Monday, the president yielded to tempatation on Thursday and told a meeting of union officials that interest rates were too high and he would "not fight inflation with your jobs." But the lapse caused a flurry among Fed-watchers.

To see the initial reaction last week, it seemed the central bank had overdone it already: The financial markets -- clearly panicked -- gyrated wildly. The dollar plunged further. Gold prices rose. The stock market plummeted 48 points in three days. And economists predicted glumly that the recession would deepen.

By week's end, however, the flailing had dissipated some and the Fed's new tightening was taken for what it was -- a bold, but most likely necessary, gamble designed to end the current speculation and stem the latest dollar slide and gold fever.

For his part, Volcker merely reiterated his promise that the board wouldn't consciously bring on a credit crunch. But, as might be expected, he was clearly unrepentant. "We captured their attention," the Fed chief gloated in his TV appearance. The following day, the market turmoil subsided somewhat.

But the doubts still persisted for the administration to assuage, and they were not mollified by Carter's comment Thursday on interest rates. The jury still is out.

All the same time, there also is some worry over whether the Fed will prove albe to recognize when its treatment has continued long enough, before too much damage is done to the economy. One of the classic mistakes in past years has been the central bank's tendency to administer its medicine too long.

There were no certain answers last week to these or any other questions about the impact of the Fed's actions, except to conclude that the next few weeks will be critical ones for the American economy. Last week's credit-tightening itself won't necessarily mean severe economic hardship.

But its failure well might.