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Supply-side economics, the only really new element in President Reagan's program, is not working as its passionate proponents within the administration had promised it would - at least not yet.

That is the President's problem, because a growing number of observers - including some within the administration - believe the theory itself is flawed.

Should Mr. Reagan jump ship of supply side economics? If he did, he would be left with the same old bag of well-worn economic tools wielded by his predecessors in the Oval Office, often to little effect.

To begin with, two schools of economic thinking dominate the Reagan approach:

* Monetarism, which holds that inflation - the economy's chief evil - can only be cured by curbing and controlling the growth of the nation's money supply.

''If Reagan sticks with the monetarists,'' says a well-known economist, ''he has nothing new. Monetarists say there is no magic way to get inflation down. You must restrain the economy and stay the course, however painful.''

* Supply-side economics, the other dominant school, is very different, holding that huge tax cuts hold the key to solving the nation's economic problems.

The larger the tax cuts, the better, the theory runs. Tax cuts - notably the three-year, across-the-board 23 percent Reagan reduction - will more than pay for themselves by generating so much investment and savings that the economy will spurt ahead.

Productivity will climb, jobs will be created, and the US Treasury will garner more tax revenues through the overall economic expansion than it lost when taxes were cut.

Key to this theory is ''savings.'' If taxpayers simply spent their tax savings, everyone agrees, the result would be inflation, as a flood of new money chased goods.

Supply-siders argue that this will not happen. ''We expect half of the personal tax cuts to be saved,'' says Treasury Secretary Donald T. Regan.

Murray Weidenbaum, the President's chief economic adviser, cites a ''host of savings incentives for 1982,'' beginning with the new liberalization of IRAs (individual retirement accounts).

Experts as diverse as Arthur F. Burns, Herbert Stein, Charles L. Schultze, Walter W. Heller, and Paul A. Volcker have warned that inflation, not savings, will result from the Reagan tax cuts - unless they are balanced by equivalent trims in government spending.

Over the next five years, as matters now stand, the tax cuts far outweigh the reduction of spending foreseen by the White House, partly because defense outlays are scheduled to mushroom.

Over the next three years, says Treasury chief Regan, tax cuts will total $ 283 billion, compared with $410 billion in budget deficits. The difference would be made up by extra savings.

There is no ''historical precedent,'' says Federal Reserve Board Chairman Volcker, for savings to be generated at such a pace.

''Supply-side economics,'' says Charles Schultze, senior fellow at the Brookings Institution, ''is absolutely ungrounded in any economic research.''

Whoever is right, the supply-side part of the Reagan program has encountered widespread skepticism, especially on Wall Street.

The investment community, says Peter G. Peterson, chairman of Lehman Brothers Kuhn Loeb Inc., looks down the road and sees enormous government deficits building up.

''Especially,'' says Mr. Peterson, ''because - as part of the Reagan tax program - the three-year tax cuts are to be followed by indexing taxes (against inflation). This alone will cost the Treasury $34 billion the first year.''

(The US Treasury now reaps an ''inflation dividend,'' as inflation pushes workers into higher tax brackets, where they owe more money to the government. Indexation, scheduled to begin in 1985, is designed to end this ''bracket creep.'')

President Reagan denounces opposition to his policies as premature, saying that his program has been in effect only since Oct. 1. While this is true, Mr. Reagan himself has long claimed that passage of his program would change the expectations of people.

''Central to the new policy,'' said the President on Feb. 18, ''is the view that expectations play an important role in determining economic activity, inflation, and interest rates. Decisions to work, save, spend, and invest depend crucially on expectations regarding future government policies.''

''Supply-side economics,'' says an expert, ''promises magic. It is the only new element in the Reagan program. If Ronald Reagan gives up on the supply-side theory, he becomes a tired old president wrestling with an intractable world.''

That may be why the President - although the economy sags and public faith wilts - may feel impelled to stick to his guns.

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