The budget deal agreed to yesterday by President Bush and congressional leaders should help bolster U.S. economic growth in the long-run, but it is not likely to provide much help in the short run for an economy flirting with recession.

By cutting into the amounts the federal government would have to borrow to finance a growing deficit, the budget agreement -- if enacted and enforced -- would leave more money available for private investment and keep interest rates lower than they otherwise would be, economists said.

The short-run question is whether the $40 billion in higher taxes and fees and cuts in federal spending proposed for fiscal 1991, which began today, will cause consumers and businesses to cut their own buying and push the weak economy into a recession.

The problem is that any immediate reduction in interest rates paid by individuals on new cars and homes or businesses financing new investments is likely to be small, financial market analysts said.

Underscoring the economy's vulnerability, the negotiators agreed on a new economic forecast that the nation, already feeling the impact of tighter credit and higher oil prices, is facing more bad news.

The new official forecast shows virtually no economic growth for the rest of the year and a 1.3 percent increase in inflation-adjusted gross national product in 1991. The forecast also shows the nation's unemployment rate, which was 5.4 percent in August, rising to 6.4 percent by the end of 1991.

"Of all the years they could have done the budget deal, this is the least appropriate," said economist Charles L. Schultze of the Brookings Institution. "But it still should be done. I only wish they had done it last year, even more the year before."

Schultze and many other economists have been urging for years that steps be taken to slash deficits to reduce federal borrowing, which they said was eating up too much of the nation's limited amount of savings. As a result, they argue, interest rates have been higher than they otherwise would have been and business investment, essential for long-term U.S. economic growth, has been held down or financed by foreign investors.

The proponents of deficit reduction are hoping that the prospect of lower budget deficits will bring down long-term interest rates. Federal Reserve officials have said they would, in effect, lower short-term rates about as much as long-term rates fall once Congress approves a deal.

Some financial market analysts have warned, however, that long-term rates might fall only by a quarter percentage point or a third of a percentage point because of the deal, particularly if there is any question about whether the deficit reduction proposals will add up to as much as negotiators claim.

Even with the announcement of an agreement, "the process is not over," said Sam Kahan, chief economist of Fuji Securities in Chicago. "Whatever agreement they have, they will have to sell that to the troops ... No matter what they publish, every one will wonder how much is real and how much is Memorex."

Bush said at the White House that unlike some past budget deals, there were no smoke or mirrors this time. "With a half-a-trillion dollars in real deficit reduction -- and let me repeat, the {congressional} leaders here and I think that these are real deficit-reduction figures -- long-term interest rates should be able to come down ... This package should be a strong component of a positive, responsible fiscal and monetary policy."

But come down from what?

Rising interest rates in Japan and Germany and financial market fears of worsening inflation recently pushed interest rates on 10-year U.S. government bonds close to 9 percent. Even with a very soft economy and the new budget deal, the administration now assumes those rates will average 8.3 percent next year. That is higher than the projection of 7.9 percent the administration used in the July forecast.

In other words, the budget deal is not expected to mean dramatically lower rates for home mortgages, new car loans or personal loans, or for business borrowers.

While even modestly lower rates could give the economy a boost, the proposed increases in gasoline, energy and payroll taxes would mean consumers would have less income left to spend for other things. Similarly, federal spending cuts would reduce another source of jobs and income for some Americans, particularly in the defense area.

The increase in gasoline and fuel taxes, expected to raise about $12 billion a year when they are fully in effect, would add about 0.2 percent to next year's inflation rate. Increases in taxes on airline tickets, cigarettes, liquor and certain luxury items such as cars that cost more than $30,000 also would add to the inflation rate next year.

In the new administration forecast, prices are shown rising 5.2 percent this year and 4.6 percent in 1991, compared with last year's 3.8 percent rate.

Brookings's Schultze, chairman of the Council of Economic Advisers in the Carter administration, stressed yesterday that he believes a budget deal should go through as soon as possible to reduce the drain of U.S. savings even though it carries with it added short-term risks for the economy.

At a conference here last week, Sidney L. Jones, assistant Treasury Department secretary for economic policy, said that during the 1980s the U.S. personal savings rate plummeted. That decline, he said, was partly responsible for "a significant erosion" of business investment in the United States "despite borrowing $100 billion to $150 billion" abroad each year.

Schultze, Jones and many other economists would like to see an increase in business investment in hopes that would improve long-term growth of productivity -- how much output is produced for each hour worked. This is the primary source of an increase in living standards. Over the past two decades, Jones said, productivity has increased less than 1 percent a year.

Other analysts said a budget deal also was needed now because the higher interest rates in Japan, Germany and some other major industrial countries are encouraging foreign investors, who have been helping finance the U.S. federal budget deficit, to put their money in those nations rather than in the United States.

Investors will be focusing this week on the credibility of the budget proposals, including how much of it might be reversed by future sessions of Congress, Kahan said. At the same time, Federal Reserve officials will be watching the market's reaction.

The Fed's top policy-making group, the Federal Open Market Committee, will hold a regularly scheduled meeting tomorrow to set monetary policy for coming weeks. If Congress approves the budget deal, the Fed is expected to bring short-term rates down -- unless "the market gives it a real thumbs down," Kahan said.

Whether because of mounting evidence of a weak economy or news that a budget deal was near fruition, long-term interest rates fell late last week. Yields on 30-year government bonds, which had been as high as 9.17 percent recently, dipped to 8.93 percent Friday.

F. Ward McCarthy of Stone & McCarthy, a financial markets research firm in Princeton, N.J., attributed the drop in rates to "the rumors coming out of Washington. The market responded very favorably ... It looks like the market is getting fairly excited about it."