President Reagan's new budget assumes that the recession will end shortly and be followed by several years of strong economic growth with falling inflation, unemployment and interest rates. Large though declining budget deficits would continue indefinitely.

Using language far less optimistic than that of last year, Reagan said, "Some seek instant relief from the economic problems we face. There is no such panacea." He described his budget as the "second challenging installment of a politically difficult, yet necessary, program."

With the business and personal income tax cuts passed last year and large increases in defense spending year after year, even continuous economic growth and large cuts in the non-defense portion of the budget would not produce a balanced budget.

In 1987 the deficit still would be $53.2 billion. Without more cuts Reagan would not be able to balance the budget even if he is elected to a second term, Office of Management and Budget Director David A. Stockman conceded.

But the rebound from the recession predicted by the administration is faster and much longer lasting than that projected by many other forecasters, who say the tight money policy called for in the Reagan budget would keep a lid on economic growth.

The administration's new economic forecast accompanying its federal budget for fiscal 1983 is sure to be contested by other economists on many points.

Even Reagan foresees a somewhat less ebullient recovery than those following major recessions in the past, which means unemployment will remain high for several years. Real output is expected to increase 5.2 percent in 1983 and 4.9 percent in 1984. The unemployment rate, which was 8.5 percent in January, is expected to average 8.9 percent this year and remain above 7 percent through 1984.

The administration also predicts a continued decline in inflation. Consumer prices, which rose 10.3 percent last year, are expect to climb by 7.3 percent this year and 6 percent in 1983.

Most private economists say they believe inflation will be higher, particularly for 1983, when they expect little additional progress to be made if the economic recovery is still under way then.

Unlike last year, the administration is not counting on a swift decline in interest rates, even if inflation comes down on schedule. The damage done to financial markets has been so severe, officials said, that "The widely anticipated decline in interest rates will not proceed as rapidly nor as predictably as many hope."

The average rate on new three-month Treasury bills is estimated at 11.7 percent this year, down from 14.1 percent in 1981, and at 10.5 percent for 1983.

In that case, corporations would probably still be paying at least 12 or 13 percent next year when they borrow money to finance major investments in new plants and equipment. Mortgage interest rates probably would be in the 14-to-15-percent range.

But some other forecasters say the combination of ever slower growth of the money supply -- the current policy of the Federal Reserve that Reagan again endorses in his new budget -- and continuing budget deficits will keep interest rates higher.

The Congressional Budget Office warned last week that there could be a clash between monetary and fiscal policy leading to "high real interest rates that crowd out private investment . . . . Given policies currently in place, the next several years promise a combination of restrictive monetary policy, designed to shrink inflation, and a stimulative fiscal policy intended to generate rapid economic growth."

Stockman, Murray L. Weidenbaum, chairman of the Council of Economic Advisers, and other administration officials consistently turned aside questions about this potential clash at briefings for reporters.

Specifically, the administration forecast calls for a rate of increase in the gross national product that appears too high to be consistent with current Federal Reserve monetary policies.

For example, from the fourth quarter of 1982 to the fourth quarter of 1983, the GNP, including inflation, is forecast to rise 11 percent. The Federal Reserve is aiming for 4 percent money growth this year and, according to the policy backed by Reagan, for less in 1983.

The gap between the 11 percent increase in the GNP and the 4 percent increase in the money supply has to be bridged by a jump in the rate at which each dollar is used over and over again in successive transactions.

Thus, the increase in this dollar turnover rate, which economists call the "velocity" of money, would have to be about 7 percent in 1983. The same arithmetic suggests that the administration is counting on another 6 percent or so rise in velocity in 1984.

However, the annual increase in velocity has averaged only 3 percent since 1954, and in only five years was it as much as 5 percent.

Asked why the administration is basing its forecast on historically high velocity growth rates, CEA member Jerry Jordan, a monetary economist, replied, "Higher than historically high . . . . "

If the velocity of money behaves in anything approaching normal fashion in 1983 and 1984, the GNP cannot grow as fast as the administration projects and interest rates will be higher, in the stated opinion of most economists.

The latest forecast of economist Alan Greenspan, a frequent adviser to the administration, is a case in point. Greenspan's forecast assumes signficantly faster money growth than current policy would allow, and he still calculates that there will be slower rates of real economic growth than the administration predicts.

This constraint shows up in the marketplace in the form of higher interest rates, the direct cause of the recessions of the last two years. If monetary policy remains unchanged to hold down inflation, the economic recovery could be aborted, perhaps as early as next winter, some economists warn.

However, the administration says in the budget, "Against a backdrop of firm budget restraint and a controlled expansion of money and credit, inflation expectations and inflation premiums will gradually recede during the period ahead, paving the way for a sustained decline in market interest rates."

In that environment, it continues, last year's "historic reduction of average and marginal tax rates . . . is expected to create major new incentives for saving, investment and productivity."

Treasury Secretary Donald T. Regan yesterday also played down the importance of the budget deficit on financial markets, saying that deficits have "no effect" on interest rates.

Using figures that were not part of the budget forecast, Regan said last year's tax cuts will lead to such a big boost in savings by individuals and businesses that it would be easy to finance the projected budget deficits and "a very rapid increase" in capital investment.

Most economists, including some inside the administration, say they believe that there will be significant pressure on interest rates if large budget deficits continue once economic recovery is under way.

Weidenbaum has made this point recently in a number of speeches, and last year Stockman told Congress that high budget deficits had been associated with high interest rates in the past.

Reagan said, "The correction of previous fiscal and monetary excesses has come too late to avert an unwelcome, painful, albeit temporary, business slump . . . . The adjustment to lower inflation and a more moderate money and credit policy did not come soon enough to avoid interest rates and unemployment far higher than we would like, and that we are working to reduce."

Administration critics are sure to claim that Reagan's present package of economic policies will not reduce either interest rates or unemployment for very long.