When President Carter raised the possibility of a 1980 tax cut in remarks six weeks ago, he said his first preference would be to cut Social Security rather than income taxes.

The idea: an income tax cut might be inflationary, while a Social Security tax cut magically would not.

All tax cuts increase purchasing power and can increase inflation. But a Social Security tax cut also would reduce labor costs, because half the tax is paid by employers. And lower costs could lessen inflation.

Thus the government could have it both ways with a Social Security tax cut; it could fight recession and inflation at the same time.

The president has squelched further talks of a cut, but many people still believe he will recommend one, and that it will involve Social Security taxes.

But as the debate begins to gain momentum, some analysts are challenging Carter's theory that a Social Security tax cut would be significantly less inflationary than other forms of tax reduction.

It has been estimated that a $20 billion cut in Social Security taxes would shave between three- and five-tenths of a percentage point from the current 13 percent annual inflation rate, a relatively small bang for that many bucks.

Critics also warn that a payroll tax reduction would reopen the battle over how to shore up the Social Security trust fund, and some see serious new risks if Congress has to face the issue again.

Barry P. Bosworth, just-resigned director of Carter's Council on Wage and Price Stability, says he doesn't think a Social Security tax cut "would have enough anti-inflation effect to be worth talking about."

And Alan Greenspan, former President Ford's economic adviser, contends that cutting payroll taxes would force the government to turn to general income tax revenues to finance Social Security and thus jeopardize budget discipline.

Greenspan argues that the current payroll tax system provides a built-in restraint on spending because it requires that Congress raise payroll taxes to increase benefits to Social Security recipients.

Greenspan said turning to general revenues to finance Social Security would "allow far greater increases in expenditures and generate more inflation. So, while there are some shortrun benefits, in the long run it will be more inflationary."

For all Carter's public caution, there seems little doubt the administration will have to consider some kind of tax cut in 1980. If the president doesn't propose one, observers say Congress may act on its own.

Apart from the question of countering the recession, statistics show that inflation and the impact of higher oil prices have left American taxpayers far behind since the last tax cut was enacted in 1978.

Economists estimate it would take a $16 million cut to make up for the effect of inflation pushing taxpayers into higher income tax brackets. Offsetting the impact of higher oil prices could require a cut of $25 billion more.

The issue, however, centers more on how to cut taxes than whether to cut them. Some analysts fear a straight cut in income taxes would fuel demand too sharply. Others want that kind of cut to help spur business investment.

There also is the question of what, if anything, to do about the big increases in Social Security taxes already scheduled for 1981 as a result of 1977 action by Congress. Some want to roll back this scheduled increase before it sparks a voter revolt.

In general terms, both an income tax cut and a Social Security tax rollback would help counter the slump in the economy. Reducing either form of tax by, say, $20 billion would infuse a sizable amount of money into the economy.

Where the two major tax cuts differ is that a payroll tax cut could have a quick impact in trimming the inflation rate, mainly by lowering business costs. The burden of Social Security taxes initially falls half on wage-earners and half on employers. The theory is that if firms can reduce their business costs by paying out less in payroll taxes, they won't raise prices as fast.

By contrast, a similar-sized cut in federal income taxes would not slow the rise in the price index.

Supporters of a cut in Social Security taxes also argue that such a rollback would reverse the recent shift in the tax system away from the progressive income tax and toward the more regressive payroll tax.

Liberals have long argued that the payroll tax is bad tax policy, because it has a greater impact on low-income wage-earners than on those in higher income brackets. In recent years, however, it's hit upper-middle-income families, too.

But the claims that a payroll tax cut will reduce the inflation rate are based on the assumption that businesses will pass all or most of their tax savings on in the form of price restraint -- a notion some analysts find dubious.

While most economists agree that a cutback in payroll taxes would have some effect on prices, analysts differ widely on how large that impact would be. Some argue the effect would be relatively minor.

Moreover, with the problems the economy is facing, there's no certainty that an income tax cut would be as inflationary as Carter administration officials imply.

For one thing, the recession may prove deeper than the White House is predicting, allowing more room for some stimulus. Second, much of the current inflation stems from supply shortages, which an income tax cut won't help solve.

If the increase in Social Security taxes scheduled for 1981 is not rolled back before then, it most likely will spur inflation even more than the 1978 and 1979 payroll tax hikes did. If Carter can avert that, the action could have a major impact.

But for all the projected benefit, proposing a reduction in Social Security taxes also could bring on a spate of political difficulties that most members of Congress so far appear loathe to take on.

First, the move again would place the administration in the position of considering the use of general income tax revenues to finance the Social Security system -- a step opposed by the chairmen of both congressional taxwriting committees.

Second, it would revive the question of how to bolster the Social Security trust fund, which already is facing new threats from the combined effects of inflation and the expected recession.

Both Carter and Congress went through months of political agony in 1977 and 1978 over how to shore up the trust fund without turning to general revenues, and some lawmakers don't want to reopen the issue at any price.