Ronald Reagan was elected president on a promise to do what economists for years had said was impossible: fight inflation and boost economic growth simultaneously.

Helped by the magic of supply-side economics, Reagan's original plan combined large tax cuts, a huge build-up in defense spending and yet a balanced budget by 1984.

Last week the president admitted to congressional leaders that he cannot meet all those goals, at least not by 1984. Three weeks earlier he acknowledged that the United States has slid into a recession. Friday's report that unemployment jumped in September to 8 percent of the work force suggests the recession could be severe.

Has the supply-side bubble burst?

Supply-siders say that it has not. Inflation and interest rates are coming down, and supply-side theorists say that healthy noninflationary growth is just around the corner. They predict it will begin next year as more supply-side tax cuts come into effect.

But others in the administration, led by Budget Director David A. Stockman, are no longer so optimistic. They believe that the enormous deficits the Reagan tax cuts entail will frighten financial markets, clash with the tight-money policy of the Federal Reserve Board, keep interest rates high and stall recovery. Stockman has thus led a fight to reduce the deficits partly by scaling back the tax cuts.

But, as supply-siders argued, giving up on the tax cuts would be giving up on the special promise of Reagan's economics. It would leave the administration with nothing more than a traditional conservative economic policy of fighting inflation with tight money and a tight budget, high unemployment and a depressed economy. And that kind of policy becomes especially hard to sustain in an election year.

Reagan will almost certainly reaffirm his commitment to supply-side tax cuts in a news conference this week. The supply-siders are claiming victory. But many economists still think that their dream of accelerating growth and declining inflation cannot happen. The tight-money policy to which the Federal Reserve is committed, and which Reagan backs, will ensure a sluggish economy whatever happens to fiscal policy, they say.

This fall's fierce internal battle over how to cope with the soaring federal deficits feared by budget officials and expected by many private forecasters is indicative of the problems for supply-side economics now that it faces real life.

The president was urged by treasury officials to stand firm against Stockman to preserve the "integrity" of the Reagan program. The administration should maintain a steady course, argued supply-side stalwarts in the Treasury Department, who had Secretary Donald T. Regan on their side.

But what should such a course be? "If the captain of the ship sets out from New York harbor with a plan of sailing north to Miami, 'Steady as you go!' will not be a sustainable policy, and that will be clear before the icebergs are sighted," Herbert Stein, economic adviser to former president Nixon, remarked recently.

Stein believes that the attempt to fight inflation and stimulate the economy simultaneously is doomed, and that the growing conflict between Reagan's budget promises is just a proxy for this deeper policy problem.

If he is right, this week's supply-side triumph may be shortlived.

Firstly, merely putting off the balanced budget for a year or two will not make the budget problem go away: the numbers are just too large. And even if supply-siders win another victory on fiscal policy in the future, their tax cuts will not neutralize tight-money policy and let the economy grow, most experts believe.

It might be natural for a captain such as Stein describes to be gripped by paralysis as he agonizes over whether to go north, or to Miami. Such a paralysis seemed to overcome the administration this fall. A full six weeks have gone by since the president announced plans for further spending cuts and some "revenue enhancement" measures. But the details of the proposals have yet to be finally announced.

Originally billed by Stockman as just a "mid-course correction," they have been mired in the larger and longer issue of how to reconcile Reagan's commitments to tax cuts, increased defense spending and a balanced budget; or, in Stein's view, the dilemma of whether to go for growth or anti-inflation retrenchment.

"The system's been on overload" with all major elements of economic policy being fought over bitterly, a participant in the battle said last week.

And as a senior White House official said, "We're down to fairly unpleasant alternatives."

Not surprisingly, Reagan apparently has opted for the least unpleasant: that of slipping the balanced budget timetable.

This is embarrassing politically. It was only recently that the president claimed that "inflation results from all that deficit spending" and described how the government's debt would stretch miles high if stacked up in dollar bills.

But it is also almost certainly true, as Reagan was reported to have said to congressional Republicans last Friday, that the American people care more about bringing down inflation and interest rates than they do about balancing the budget. They may happily accept his retreat from a balanced budget if he now tells them a balanced budget is not the route to lower inflation.

A Treasury Department supply-sider last week said that people only really care about the balanced budget as a shorthand for cutting government spending. But it is probably just as likely that people only want to cut spending because they believe that will help control inflation.

Just as the deepening recession has led almost everybody to oppose tax increases in 1982, it also threatens to dissipate what little enthusiasm there is in Congress for further deep spending cuts.

Reagan and his treasury team say the search for more budget cuts must be stepped up at the same time as they denounce tax increases during a recession. But spending cuts depress the economy just as surely as do tax increases.

The president's decision to postpone the balanced budget, but leave his other goals and policies intact, ignores the political difficulty of making further deep cuts in domestic spending programs and the prospect that by 1983 and 1984 the federal deficit may be frighteningly large. It thus merely postpones, and does not resolve, his budget problem.

If Reagan this week still refuses to contemplate extra tax increases or large cutbacks in defense spending in 1983 and 1984, then budget analysts, not to mention Wall Street financiers, will expect the problem to rear its head again soon.

New Office of Management and Budget forecasts predict a $100 billion deficit in fiscal 1982, rising to almost $150 billion by 1984. Other budget experts believe that these numbers are plausible. They say that Congress, urged on by the president, simply cut taxes too much this summer.

For months, virtually nobody outside the administration has expected a balanced budget in 1984. But economists, whether conservatives such as Stein or liberals from the Brookings Institution, also predict that taxes will have to be raised before then. The deficits will otherwise be so large as to create almost intolerable strains in financial markets.

If supply-siders win another policy victory in the next administration battle over the budget -- and Stockman is bound to continue fighting for restraint -- then it will be clear that Reagan is going for fiscal stimulus and growth rather than a conservative fight against inflation.

But if the Federal Reserve keeps the monetary brakes on, this will be asking for financial trouble. It may also lead a Congress still anxious about deficits to take budget and tax policy out of Reagan's hands.

One obvious way for congressmen to narrow the budget gap would be to postpone Reagan's supply-side tax cuts: if not the 10 percent cut due next summer, then the next phase in 1983.In that case, supply-siders would be losing the policy war, even if they win the battle within the administration.

Monetarist Rudolph Penner of the American Enterprise Institute is more optimistic than many economists about next year's recovery. But last week he said that another "confrontation between recovery and monetary policy" is likely next year as the economy runs into the low money ceilings set by the Federal Reserve. Such a confrontation would send interest rates soaring again, and, of course, would choke off the boom.

It is just this outcome that senior budget officials dread. Stockman argued to Reagan this week that without new and believable measures to shrink the deficit, a 1982 recovery -- nicely timed for the elections -- would lead straight to an electorally disastrous increase in interest rates.

But the treasury supply-siders warned Reagan that without the tax cuts enacted last summer there would be no strong preelection recovery from the current recession.

Fiscal policy this year is indeed mildly contractionary, White House economists calculate, despite the yawning deficit numbers. These largely reflect the automatic effects of recession, which cuts government tax revenues and increases spending on income-support programs.

When private sector demand is pushed down by recession, it is also easier to finance the government's deficit. In order to calculate the underlying, or structural, budget deficit, economists abstract from the effect on the raw numbers of the business cycle.

However, next year the fiscal balance shifts, largely under the impact of the scheduled tax cuts. Even if Reagan won the further $115 billion in spending cuts and tax increases in 1982 to 1984 that his September proposals assumed, policy would begin to swing towards expansion with next summer's scheduled tax cuts, gathering momentum in 1983 and 1984. If he does not get these further savings, then the structural, high-employment deficit would yawn wider in those years.

Conservatives like Stein see nothing wrong with fighting inflation in the traditional way. "The economy needs to be slowed down in order to check inflation," he says. He, and many others of like mind are concerned first to reduce inflation and then to see whether the economy can manage to grow healthily without rekindling it.

But many economists believe that this way of fighting inflation will cost too much in terms of unemployment and economic pain. Prof. William Nordhaus of Yale University last month said that to get inflation down to about 3 percent would take 8 percent unemployment "as far as the eye can see."

Supply-siders say they do not want to fight inflation with a depressed economy and high unemployment. But their support for tight money belies that.

Tight money acts against inflation by restricting the overall room for growth. Real output is usually slowed before prices, and it is through the mechanism of slowing the economy that tight money feeds through to smaller price rises.

Ironically, Reagan may not be able to stop the anti-inflation policy and stimulate the economy even if he wants to. A determined Federal Reserve, keeping a tight grip on credit, will likely see to that.