President Carter has ordered a stringent spending crackdown for fiscal 1980, designed to slash the federal budget deficit that year to $37.5 billion - more than $12 billion below the $50.8 billion red-ink figure now projected for fiscal 1979.

The fiscal 1980 plan would imply virtually now new spending or tax-cut initiatives, and spending cuts in some existing programs. Actual outlays for any national health insurance program inacted next year, for example, would be put off until late 1980.

The austere budget target, approved personally by Carter is an initial planning meeting on the fiscal 1980 budget, would mark a significant further tightening from the fiscal 1970 spending plan the president proposed in January, which already was considered tight.

The budget plan calls for holding total federal spending to about $538 billion, some $12 billion below what budget-makers say would be needed to continue present programs intact. After allowance for inflation overall spending would grow by about 1 to 2 percent.

By comparison, the $500.2 billion budget Carter submitted in January - which many analysts regarded as austere - provided for spending levels $7.8 billion above what would be needed to continue existing programs. After adjustment for inflation, outlays were up 2 percent.

The tight spending holdown reportedly was agreed to by all of Carter's top economic advisers. Officials say Carter has not yet decided which programs would be pared. The budget making process is expected to go on through next December.

The move was partly in response to criticism over the growth of the federal budget deficit between fiscal 1978 and 1979. Many economists believe the deficit should be declining, not increasing, when the economy is in the midst of a recovery.

In its January budget, the administration projected the fiscal 1979 deficit at $60.6 billion, virtually unchanged from the current year's $61.8 billion red-ink figure. Carter blamed the bloated deficit for fiscal 1979 on the need for a large tax cut.

Carter sought to reverse that trend by agreeing two weeks ago to trim $5 billion from his $25 billion tax cut proposal. Changes by Congress and the continuation of a spending shortfall have trimmed the deficit to $53 billion for fiscal 1978, followed by $50.8 billion in fiscal 1979.

If Carter is successful in holding the deficit to $38 billion in fiscal 1980, it would put the administration back on track toward approaching a balanced budget in fiscal 1980. Carter set such a deadline earlier, but then abandoned it as unrealistic.

However, economists both in and outside the administration still remain skeptical that the White House can balance the budget that soon. And liberals are almost certain to denounce the new spending plan for leaving too little room for new programs.

The stepped-up austerity drive appeared to have been spearheaded by James T. McIntyre, the President's budget director, with the backing of W. Michael Blunenthal, the secretary of the treasury. McIntyre reportedly had called for an even-tighter spending rein.

Sources said the basic decisions on the fiscal 1980 budget were made by Carter at an initial session last week. Top administration economic officials held a second meeting yesterday to confirm the targets and set spending ceilings for individual agencies.

Establishment of the initial targets is the first step in a lengthy budget planning process the admininstration employs each year. The fiscal 1980 budget will be presented by Carter next January in a formal message to Congress. Fiscal 1980 begins Oct. 1, 1979.