President Carter has asked his aides to come up with at least $20 billion worth of spending cuts this week that would allow him, if he chooses, to balance the 1981 federal budget.

Balancing the budget, along with other policy changes that might include some form of credit controls but not wage and price controls, officials said, would provide a dramatic gesture that the administration is serious about curbing inflation.

Cuts of that magnitude are sure to be political dynamite in an election year, and Carter might not decide to propose all of them, the sources said.

As part of a broad economic policy review begun a week ago, all federal agencies were asked on Friday to report by tomorrow morning where they would prefer to make cuts in their programs.

When Carter sent the 1981 budget to congress only a month ago, the prospective deficit was put at $15.8 billion. Now reestimates of the cost of some programs indicate meeting the balanced budget goal will take cuts of close to $20 billion, even though revenue estimates are rising too, officials said.

Senate Majority Leader Robert C. Byrd Jr. said yesterday that achieving a balanced budget would be "like pulling teeth. There will be a lot of us who would much rather go to the dentist" than make hard decisions on where to cut spending.

"We will balance the budget," Byrd declared, "but there is . . . no snake-oil remedy. It's easy to vote for a resolution . . . but the anguish comes when the hard choices have to be made."

On Friday, James McIntyre, director of the Office of Management and Budget, gave each agency a "stiff" dollar target for cutting its so-called controllable programs -- those under which spending is not absolutely required by law -- in 1981, an administration official said.

The size of the requested cuts varied from agency to agency, but some were told to find ways to cut at least 10 percent from their spending totals.

Much smaller cuts for fiscal 1980, which is nearly half over, were sought, too, sources said.

McIntyre deliberately made no suggestions about which controllable programs should be on the list for cuts.

OMB itself is examining the handful of new programs Carter proposed in the 1981 budget to see if the initiatives should be postponed or trimmed, the official said. The major domestic initiative Carter asked Congress to approve was an expanded youth employment program expected to cost $300 million in 1981 but $2 billion in later years.

Separately, administration officials also are debating whether to ask Congress to cut the automatic cost-of-living increases in federal benefit programs, such as Social Security, from 100 percent of the rise in the consumer price index to 75 percent or 80 percent.

The urgency with which the administration is approaching this policy review was underscored by the very brief period that agencies were given to respond to McIntyre's request.

Since the 1981 budget went to Congress, inflation has worsened. The consumer price index rose at more than an 18 percent annual rate in January even though food prices didn't go up at all. The February and March increases are expected to be nearly as great.

Moreover, price jumps occurred virtually across the board, not just in energy. The index of producer prices, which rose even more rapidly, showed the cost of industrial goods soaring, too.

This dose of bad news, coupled with further evidence that the economy is not yet dropping into a recession and estimates by many economists that the 1980 and 1981 Carter budgets were not sufficiently tight, sent financial markets into a tailspin.

Chaotic conditions in the long-term bond market, for instance, were stabilized last week only on the basis of a rumor that Carter was about to impose credit controls.

Officials have been hoping to wrap up their review with an announcement of policy changes by the end of this week, but one said yesterday, "I strongly doubt we will be able to do it."

One reason is that the new slashes in spending are sure "to raise all the hornets around town," he said. Each of the spending programs has a constituency, and each group will try to use their added leverage in an election year to head off reductions in their programs.

At the Agriculture Department, for instance, chief economist Howard Hjort said Friday that candidates for spending cuts include programs covering rural housing, community facilities, business and industrial expansion, farm storage facilities and commodities.

Farm groups and congressmen from farm areas are sure to protest such cuts, just as they have the decision announced Friday not to pay farmers $300 million this year not to grow crops on portions of their land. Such a plan was considered to help prop up grain prices after the embargo on further sales to the Soviet Union.

Word was spreading around the country yesterday that the National Institutes of Health was asked by OMB to find ways to trim its spending by 10 percent. Efforts to lobby against such a large reduction were already underway yesterday.

Rumors about other administration decisions abounded but so far most of them apparently are unfounded.

Late last week government employes began to spread the word that a federal hiring freeze was in the works, probably to be announced Tuesday. As of yesterday, a White House official said, no such freeze had been decided upon. A hiring freeze might well be part of the final package of changes the president announces, but it is unlikely it would be imposed separately, he said, because of the need to make the policy changes together for maximum impact.

Aside from the need for dramatic gestures to reassure anxious financial markets, administration economists, like many of their private counterparts, are pondering whether fiscal and monetary policies need to be tightened further to make sure a recession occurs.

As a practical matter, it is too late to make significant changes in the 1980 budget and affect the economy this year. That means most of the burden will have to fall on monetary policy if the administration decides more restraint is needed in real terms, not just as a psychological ploy, analysts said.

Credit controls -- which the Federal Reserve Board opposes -- rather than further increases in interest rates, controls already at record levels, are under study. Controls could immediately reduce the availability of credit, both to business and consumers, and slow the economy, analysts argued.

Since there are virtually no signs of excessive demand anywhere in the economy that could be adding to inflation, under normal circumstances there would be no need to resort to a recession to curb soaring prices.

The administration's goal for 1980 originally was just put enough slack in the economy to prevent a sharp acceleration of wage increases on the heels of last year's 13.3 percent inflation rate.

Again, under normal circumstances, the doubling of oil prices last year, which added sharply to inflation, would have pushed the economy into a recession. But consumers have continued to spend money as if the drop in their real incomes forced on them by the OPEC cartel had not occurred. They have dipped into their savings to maintain their standard of living.

The change in behavior has left the impression, in financial markets particularly, that the administration has lost all control of the economy.

Now the Carter economists must come up with a set of new policies to convince a skeptical financial community and the public at large that they can control the economy. Turning that trick probably will take nothing less than a full-blown recession, as perverse as that seems.

As economist Otto Eckstein of Date Resources, Inc., put it last week, "Without recession, there is no prospect for inflation improvement." Without that prospect, many analysts are convinced, the Carter administration cannot, in fact, regain control of the economy.