The most extraordinary rally in stock market history, coupled with President Reagan's remarkable victory on the $98.3 billion tax bill, sent administration spirits soaring last week.

With interest rates plunging and the stock market rising, Republican

NEWS ANALYSIS prospects for the Nov. 2 elections suddenly looked better. But what has really changed from a week ago?

* Prospects for the economy remain bleak. The recession is bottoming out, but analysts expect a weak recovery this fall, leaving unemployment near its postwar peaks.

* Interest rates have fallen sharply, but this decline is largely a reflection of how depressed the economy is. Many economists say rates will head back up as the economy gets off the ground, although they may not return to the heights reached earlier this year. In addition, the sharpest declines have come in short-term rates, rather than the long-term rates that affect business spending plans the most.

* The Federal Reserve Board is still committed publicly to a tight monetary policy, which will limit the speed and extent of any recovery this year and next.

* The tax bill has narrowed prospective budget deficits, but the deficits remain too large, according to most analysts, and are still in conflict to some extent with the Fed's tight money policy. Further deep spending cuts, and perhaps more tax increases, almost certainly will be needed next year to bring the deficits after 1983 below $150 billion.

* The stock market is up an astonishing 81.24 points from a week earlier, but it is still below its level of a year ago.

However, good cheer in the White House may not be misplaced. The underlying problems of the economy are now covered with a froth of better news, which may last at least until November.

Lower interest rates, as long as they continue, will foster hopes that the administration's economic program will work to revive jobs and output.

Moreover, the economic news in coming weeks probably will be better than it has been for months. A feeble recovery, or at least an economy that is not sinking further, would be an improvement over falling output and sharply rising unemployment.

The unemployment figures, which have brought little but bad news for the administration so far, may blip downward in August or September for technical reasons, according to economist Otto Eckstein.

There has been striking progress in the last year on one of the administration's major policy goals: reducing the rate of inflation. The recession, together with a strong dollar, a weak oil market and good harvests, has halved the rate of inflation over the last two years. This dramatic slowdown has helped raise the spending power of many of those who have work.

These factors, in particular the sharp drop in interest rates since the beginning of last month, have reduced "from near zero to negative" the chances of any change in economic policy before the election, one administration official commented last week. The search for a pre-election panacea for high interest rates had not produced any plausible policies that Reagan could accept, sources said.

However, one reason for the cheer in financial markets last week was a widespread perception that there already has been a change in the president's economic stance. His vigorous, if delayed, support of the tax bill was seen by many in the markets as a return from the outer reaches of supply-side economics to a more orthodox Republican view.

"The financial community had become disenchanted by Reagan's economic program, by the misguided lunatic fringe approach," Donald Trott, chairman of the investment policy committee of A.G. Becker, said last week. "But in his persistence on the tax bill he has telegraphed to the financial community that he is no longer being held hostage by this fringe element."

The president's shift on taxes came after weeks when the White House seemed happy to leave economic policy-making to the Republican leadership in the Senate.

It was the GOP senators, led by Pete V. Domenici (N.M.), Robert J. Dole (Kan.) and Majority Leader Howard H. Baker Jr. (Tenn.), who eventually convinced Reagan of the political need for major revenue increases.

High interest rates and continued sluggish growth in the economy, meanwhile, strengthened the hand of those senior advisers arguing on economic grounds for sterner measures to cut the deficit. Fear of deficits was the main reason for Wall Street's unhappiness, they argued.

The president now worries more about deficits than he did six months ago, Murray L. Weidenbaum, departing chairman of the Council of Economic Advisers (CEA), conceded last week. But it is far from clear that he worries enough to make the further changes in his program that many believe necessary.

The underlying budget problem that has faced the administration all along has been diminished by last week's tax vote, but it has not disappeared. It is simply not possible to cut taxes, increase defense spending and reduce the deficit at the same time, without cuts in domestic spending programs that have so far proved to be politically impossible.

Reagan is likely to balk at another round of tax increases next year, several administration officials said last week. And this summer he reaffirmed his commitment to his planned defense buildup. Weidenbaum reportedly tried hard to talk the president into scaling back the proposed increase in military spending. Office of Management and Budget Director David A. Stockman also has fought for cutbacks at the Pentagon.

But one Reagan supporter said last week, "Remember, there's a very strong defense secretary out there, who isn't exactly keen on cutting anything." Even though CEA Chairman Martin Feldstein is expected to be more forceful than was Weidenbaum, and several key Treasury supply-siders who played down the importance of the deficit have departed, Defense Secretary Caspar W. Weinberger still may hold the balance of power.

Last week financial markets were willing to cast all these worries aside. The prediction by Wall Street economist Henry Kaufman of lower interest rates ahead sparked the first tremendous rally in stocks, and the passage of the tax bill gave a further boost to the market Friday.

The promise of lower interest rates was apparently enough to entice buyers of stock, even though Kaufman's prediction was based on a much gloomier assessment of the economy.

The bond rally "was really based on a duller view of the economy," economist Eckstein remarked, which in turn suggests dismal profits figures and a poor outlook for industrial expansion. Eckstein and Alan Greenspan, CEA chairman under President Ford, last week said there was an even chance that the economy would be down rather than up in the July-September quarter.

"There is just no credible evidence that the upturn is under way," Greenspan said, although he added that the turnaround in financial markets could set the stage for it.

The key to the economy's growth in coming months probably lies with monetary policy. Some analysts say they believe the Federal Reserve, worried by continued weakness in the economy and mounting evidence of financial strains and cracks in the banking system, shifted to an easier policy last month.

Others say that the Fed was just responding to much weaker money supply figures when it began to supply credit more generously to the banking system, encouraging lower short-term market rates, and then lowered its discount rate swiftly.

Lower money growth allows the Federal Reserve more room to ease credit conditions without threatening its targets for money growth over the year. It also probably reflects a more depressed economy, as business and individuals cut back on their credit demands.

Whatever the true explanation, the result of Fed policy in recent weeks has been to help rates to fall. This should be enough to get the long-awaited economic recovery under way. The question is whether policy will remain easy enough to let it continue.

The odds remain that the Fed will be wary of encouraging very rapid growth or of allowing its monetary targets to be breached, at least for long. However, Chairman Paul A. Volcker has emphasized that the monetary targets are intended to give room for a modest economic recovery this year and next.

Last week's tax increases and spending cuts helped dull the supply-side gloss of Reagan's economic program. They left fiscal policy much less expansionary than it had promised to be, and thus more in line with the Fed's anti-inflationary money policy.

Reagan's economics policy no longer holds the supply-side dream of a booming economy alongside slower inflation.