High interest rates are the stick that drove Congress and the White House to negotiate all spring over the budget and that may yet push Congress to take some action to reduce the upcoming deficit.

The theory is that lower prospective deficits will reduce pressure on the financial markets, reduce fear of future inflation, and for both reasons bring a reduction in interest rates that will let the economy off the floor of recession.

But there is a problem: the theory may be wrong.

All sides agree that high interest rates are a leading cause of the economy's problems. But there is lively disagreement about the rest of the equation: just what is keeping rates high now, and how best to bring them down without harming the economy in other ways.

President Reagan has himself been afflicted by this split in opinion. Thus he has said that the likely deficits over the next several years are keeping rates high, in part because they are raising inflationary expectations and leaving investors unwilling to lend except at extremely high rates. But he has also taken a contrary view and, citing cases in the Midwest where local banks have cut their rates, has argued that interest rates should come down because the inflation rate has come down so much in recent months.

There are several lines of argument against the interest rate theory on which the budget negotiators have been operating.

The first says a lower deficit might indeed mean lower interest rates, but the tax increases and spending cuts that Congress would have to vote to reduce the deficit could hurt the economy more than the lower interest rates would help it.

A related argument says that it is monetary policy, rather than budget deficits, that is mainly responsible for keeping interest rates high. The Federal Reserve Board's tight money policy, which Reagan supports, will keep the cost of money unusually high no matter what happens to the deficit, this argument goes.

If the deficits contribute to the demand for credit, the Fed controls the other half of the equation: the credit supply. If the Fed changed its money policy, and announced that it intended to bring interest rates down, "they would fall like a shot," Wall Street economist William Griggs of J. Henry Schroder said last week.

There is yet another view that says a budget compromise that reduces the deficits in 1983 or later may not have much effect on interest rates today. These are kept high more by the Treasury's large borrowings in the present and the immediate future than by deficits in later years, the argument goes.

On the first point, Brookings Institution economist George Perry has said he would not be disappointed if the budget talks broke down. He said that many of the proposals under discussion--such as postponing cost-of-living adjustments for Social Security and other federal benefits due in July, or imposing an oil import fee--would dampen the economy more than any consequent fall in interest rates could stimulate it.

A monetary economist, who has looked at the relation between deficits, interest rates and the economy's total output or gross national product, agreed. With no change in monetary policy, he calculated, tax increases and spending cuts of the size that the negotiators were considering would bring interest rates down by just under 1 1/2 percentage points in 1983. But even with lower interest rates, the net effect on the economy of the $65 billion in tax increases and spending cuts that he assumed in 1983 would be to reduce real GNP by 2 percent.

Projecting to the middle of 1984, this economist said the tax increases and spending cuts would amount to more than $100 billion. That large a budget compromise would cut more than 3 1/2 percentage points from the interest rate on three-month Treasury bills, he said. But with consumer spending and business investment hit by higher taxes and less government spending, the GNP would be 3 1/2 percent lower than with no compromise and higher interest rates.

Others believe that cutting the budget deficit would have a bigger impact on rates than that, even if the Fed did not ease up on money. Treasury Secretary Donald T. Regan told reporters Friday that interest rates on three-month Treasury bills would have been cut by 2 1/2 percentage points by 1983 if the negotiators had agreed on a compromise to bring that year's deficit down to about $110 billion.

Such a reduction would still leave rates quite high by historical standards. With the inflation rate now as low as 6 percent or 7 percent, interest rates are at least 6 percentage points or more above the rate of inflation. Historically, the differential between inflation and interest rates--or the "real" rate of interest over and above the return that compensates lenders for inflation--has been closer to 2 or 3 percentage points.

The recession also should have brought rates down, according to the patterns of the past. As the economy slides in a recession, the private sector's demand for credit normally falls off. Consumers and businessmen are less willing to go into debt, and try to pay off outstanding loans if they can. This lessens pressure in financial markets and reduces rates.

To explain why interest rates are not behaving as they have in the past, analysts have pointed to the policy differences between today and previous periods. But with both fiscal and monetary policy now very different from before, experts disagree about which is having the most effect.

Those who believe deficits are the main culprits split roughly into two groups. One believes that today's high interest rates are related less to future deficits than to the government's credit needs today and for the rest of this year. This view holds that a budget compromise affecting later years would have little impact on today's market.

One administration official, who strongly favors cutting the outyear deficits, nevertheless said recently that he would not expect this to bring interest rates down much in the near term.

But another group argues that future deficits are having an impact on today's markets, and in particular are keeping up long-term bond rates. This works primarily through expectations. Investors who have been burned many times by higher-than-expected inflation--which has cut the value of the long-term bonds they are holding--are especially cautious about betting on lower inflation. They fear big deficits in the future may reignite inflation and push the Fed into easing its money policy, the argument goes, so they demand high rates on long-term money.

Perverse though it sounds, some also argue that if the Fed were to shift to an easier monetary policy this might drive interest rates up rather than down, because it would add to investor fears of future inflation.

Fed Chairman Paul Volcker said last week that a decade or more of accelerating price rises had "left a scar" on the behavior and expectations of savers and investors. Volcker says the best way to heal that scar is to bring down deficits, and stay firm on money policy.

But others believe that the only way to bring interest rates down and at the same time boost the economy is to ease money policy. Irving Auerbach of G. Aubrey Lanston & Co. Inc. said last week that rates are high because of the Fed tight money policy. Short-term interest rates are dominated by Fed policy, he said. As the Fed keeps a check on money growth by adding money only slowly to the banking system, banks are forced to pay higher rates for the funds they need and this puts upward pressure on all short rates, he said.

With short-term rates high, there is no incentive for people to lend money longer term at lower rates even if they are not worried about future rises in inflation, he said.

Auerbach thinks the Fed is right to keep money tight, for as long as Congress and the administration fail to reduce the long-term budget deficits. But this is because he believes a looser Fed policy, while it would bring rates down, could lead to higher inflation when combined with big budget deficits.

Many of those who argue for smaller budget deficits to help the economy also assume that the Fed would then allow more money growth. Easier money would then help bring interest rates down enough to offset the dampening effect of the tax increases or spending cuts aimed at narrowing the budget deficit, they say.

The catch is that Volcker has not indicated that he will play along with such a bargain. He repeated last week that he believes there is room within the Fed's present money targets for the economy to pick up later this year. His monetary policy may still be aimed primarily at fighting inflation, whatever happens to the budget deficit. In that event, a budget compromise might not reduce interest rates as much as some leaders in Congress believe.