The Carter administration is embarking on a major shift in the broad "comprehensive" economic policies it adopted last January: It is moving to tighten the amount of fiscal stimulus to the economy to help combat inflation.

The change began in mid-April, with an internal debate that led to President Carter's recent decision to trim the size of the $25 billion tax cut he proposed last winter by $5 billion and to postpone its effective date until early 1979.

Last week, Carter himself completed the shift by approving a tight clampdown on spending targets for the fiscal 1980 budget being put together now designed to reduce the deficit that year to $37.5 billion as part of a long-term belt-tightening exercise.

By week's end, key administration officials were letting it be known the president is so serious about slashing the deficit that budget makers even are looking for potential cutbacks in the fiscal 1979 spending plan Carter submitted in January. Those savings could amount to $2 billion to $5 billion.

The decisions mark a major turnabout from the policy course the administration laid out in January - a hold-the-line posture on government spending programs combined with significant new economic stimulus from a $25 billion tax reduction package.

Carter said then his proposals were intended to lay out a comprehensive economic plan to eliminate the continual policy flip-flops for which the administration was criticized in 1977. Now, barely four months later, the administration has flip-flopped again.

What were the reasons for the latest Carter turnabout? On the surface, there seemed little genuine economic reason to shift policy. Although inflation last quarter was more rapid than expected, most of that was in food prices, which aren't affected by deficits.

And although the administration faced a changing political climate - stemming from new voter concern over inflation - the forecasts still show the economy will weaken some in 1979, calling for continued stimulus. The administration had good reason to holdits ground.

Rather, what appeared to spark the turnabout was mounting concern by top policy makers over the danger posed by a new element in the overall economic picture - the abrupt tightening of money and credit policies by the independent Federal Reserve Board.

Prodded by its own fear of inflation - and the need to help stem the decline of the dollar - the board had begun pushing interest rates up sharply. Alhough the squeeze hadn't hurt seriously yet, key Carter economic advisers feared the worst if the tightening should continue. The specter of a crunch lay ahead.

What's more, policy makers finally concluded there was room to rein in a bit if needed. Charles Schultze, the president's chief economist, told reporters the economy seemed to be rebounding beyond mere recovery from the coal strike. And unemployment had plunged far more rapidly than expected.

What the administration has done in effect is to cut a deal with the Fed's new chairman, G. William Miller: The White House will begin tightening fiscal policy, with the understanding that Miller won't let interest rates rise too sharply. If Carter is successful, Miller will ease policy more.

The accord isn't formally in writing, but both sides essentially have confirmed it. In an unusual move, the White House specifically sought Miller's endorsement of its tax-package decision two weeks ago before formally announcing it. And Miller publicly has praised the new tight-budget plans.

The question is whether either side actually will be able to deliver in this fragile bargain.

Although Miller has proved to be an influential spokesman for the Fed in his few months as chairman, he still is only one member of a 7-person board, and one of 13 on the Federal Open Market Committee, which sets short-range interest rate policy.

There is no doubt a sharp cutback in the budget deficit would ease pressure for a tight-money policy, but knowledgeable observers say FOMC members are deeply fearful that inflation is accelerating over the longer term. Even if budget policy does turn restrictive, Miller may not get what he wants.

And whatever members' private feelings are about monetary policy, the board still has a historic commitment as the nation's chief institutional inflation fighter and defender of the dollar overseas. And much of the Fed's actions on interest rate policy follow the market, rather than lead it.

At the same time, the White House is limited by the traditional foibles of the American budget making process: No matter what spending cuts the president proposes, it still is up to Congress to approve or reject them. And the lawmakers still haven't shown much stomach for cutting back pet programs.

The $37.5 billion spending target the president approved last week for fiscal 1980 may seem very draconian to many budget experts, but history shows it may be difficult to win approval of the individual spending cuts that total represents.

Indeed, Carter has had enough trouble getting Congress to follow the fiscal policy he proposed last January. The lawmakers, troubled by inflation before the president was, effectively cut his tax package before the White House finally got around to agreeing on it."

Ironically, what may save the president is the refiguring done by Congress as part of the new congressional budget process. Every year, the lawmakers manage to hold spending below the administration's original January target by reshuffling some key programs and eliminating White House budget padding.

There also is the benefit of the continuing spending shortfall, which consistently leaves actual outlay levels well below start-of-year targets.

Whatever the outcome of the Carter-Miller agreement, the new policy turn about will have one sure result: There will be even less room for the major new spending programs Carter promised during the 1976 campaign - particularly a national health insurance program, which is costly by any standard.

Whether the administration ultimately will be proved correct in its latest policy shift won't be known finally for a good many months. The judgement will depend on how the economy fares in 1979 - both on the inflation side and on staving off an economic slowdown - with a less-stimulative policy.