A month ago President Reagan left Washington in triumph; last week he came back under a cloud created by high interest rates, tumbling stock prices and ballooning budget deficits. What happened?

Economists can argue that question at length, but in political terms the answer is straightforward. During August, the promises the Reagan administration had made about the impact of its economic policies lost plausibility. This fall, Reagan will have to begin explaining why those promises cannot come true any time soon.

The promises were made last winter, when Reagan and his aides introduced their "economic recovery program." They said that a combination of budget and tax cuts would transform the national psychology and help bring on brisk economic growth, tumbling interest rates and sharply lowered inflation, leading to a balanced federal budget in 1984.

Today those promises all seem out of reach, which is the basic reason investor confidence on Wall Street is low and declining, instead of booming as Reagan's men predicted last winter. Low investor confidence helps ensure high interest rates, and high interest rates frustrate the economic recovery program.

High interest rates also drive up the expenses of the federal government, the nation's largest borrower. So, unwelcome economic developments have contradicted the predicted consequences of enacting Reagan's program and have created a need for a new, more painful round of budget reductions.

The president's men came to appreciate their new dilemma during the Parisian-style August recess that Reagan gave Washington. They are scrambling to find new ways to cut federal spending further in hopes of redeeming the promises they made last winter, when the new administration was riding on the quadrennial wave of euphoria that Americans like to wrap around new presidents.

So the administration has decided it must reconsider one of its earliest policies, an unrestrained and enormous arms buildup. And the White House will launch another campaign to cut the federal budget for 1982, the same budget from which Congress took $35 billion earlier in the year.

In political terms, some administration officials are pleased at the prospect of reopening the budget fight, which they won so decisively during the spring and summer. Budget-cutting is obviously this administration's strong suit, and the White House is happy to keep playing it.

"If we didn't renew the battle" over the budget, one official said, the federal agencies and congressional committees would probably get the idea that the pressure was off and they could revert to freer-spending ways. Moreover, this official said, if Congress ever finishes the budget it will have time to turn to controversial social issues that won't do the administration any good politically.

But a return to the budget-cutting crusade, even if successful, won't solve the administration's overall economic problem, which is this: budget cuts made or suggested so far won't be big enough to finance the expanded defense program and offset the huge new tax cuts Congress adopted.

Instead of steadily shrinking deficits leading to an early balanced budget, there is a danger of budget deficits much larger than Jimmy Carter's, and Wall Street knows it. If anyone still doubted, The Wall Street Journal ran a front-page article last Monday reporting private forecasts that the budget deficit could be $100 billion a year for each of the next several years.

According to sources inside the Office of Management and Budget, David A. Stockman, the mastermind of the economic recovery program, never really expected Congress to pass a tax cut as big as the administration had requested. Moreover, Congress added a provision indexing taxes to inflation from 1985 onward.

Only after that action, these sources report, did OMB technicians look seriously at the tax cut's fiscal implications. They quickly found that under current economic conditions, especially high interest rates, the forecasts leading to a hypothetical balanced budget in 1984 could no longer be defended. That realization prompted the apparent decision in principle to make cuts in the previously untouchable defense budget.

Even before those calculations were made, however, senior administration officials most intimately involved in the economic program permitted themselves occasional private moments of despair.

"In the beginning everyone said we were trying to do too much," one of them said, sounding pained. "Now that we've done all of it, it's obvious that we didn't do enough" to cut federal spending. These officials are particularly chagrined that they at first excluded Social Security, a huge drain on the federal budget, from all cuts, then suggested a clumsy set of Social Security cutbacks that set off a political uproar.

"They fooled themselves," said W. Bowman Cutter, third-ranking official in Carter's OMB. In an interview Cutter noted that, in their forecast for the 1982-'86 period, Reagan aides foresaw a 22 percent higher economic growth rate than Carter's last budget did, a 28 percent lower rate of inflation and 20 percent lower interest rates. Those "weren't a forecast, but a vision," Cutter said.

The administration now plans a renewed political battle that will involve revoking deals made earlier in the year on Capitol Hill to win passage of the budget and tax cuts, and will also dig into popular federal programs.

If Stockman and the senior White House aides have settled on a strategy for this battle, they haven't shared it with their subordinates. Next week a series of Cabinet meetings is scheduled to work out final proposals for the new round of cuts.

In the first phase of the Reagan administration, the new government was held together by a remarkable unanimity. Now there is open warfare between senior White House aides and the secretary of defense over possible spending cuts. And some of the Republicans in the House who swallowed hard to support budget cuts last winter are indicating that they may not go along again.

The administration has a new kind of problem in its reexamination of the budgetary situation. If the economy is not going to boom as the White House predicted last winter, cuts of $20 billion to $50 billion a year more than anticipated will be needed to show a decisive reduction in the deficit, and even more than that to balance the budget.

But cuts of that magnitude, OMB officials acknowledge, can come only at the expense of the administration's huge defense program, or by dramatically altering the federal government.

In 1981 the discretionary, non-defense budget-- that is, money for programs that are not legal obligations like Social Security and Medicare -- accounted for 17 percent of total spending.

By the Reagan administration's earlier optimistic projections, that part of the budget will fall to 11.3 percent of the total in 1986. This would represent a fall from $111 billion to $78 billion for all the government's grant programs, such as space exploration and highway construction.

Shrinking the government that far would be a problematical business, and anything deeper could be revolutionary. And bigger cuts overall would almost certainly require digging deeper into this politically popular part of the budget.

Cutter of Carter's OMB has added up the numbers and argues that, unless there are huge savings in defense or the big entitlement programs like Social Security, Reagan may be forced to ask for enormous cuts in the discretionary non-defense sector.

Cutter said he could imagine proposals to reduce the federal work force in that realm from today's million or so to 600,000, with commensurate cuts in the programs.