Plagued by high interest rates, collapsing markets and fast declining profits, businessmen are slashing their plans to invest in new plants and equipment, jeopardizing a key element of the Reagan economic program.

A Commerce Department survey released yesterday showed businesses plan to invest 2.4 percent less this year than they did in 1981, after adjustment for inflation. The new survey indicates a sharp reversal in business spending plans since the start of the year.

Most private forecasters expect the actual cutbacks in investment will turn out to be even larger than shown by the survey.

If inflation is included, executives of non-farm businesses said they plan to spend $328.6 billion on new plants and equipment this year, up 2.2 percent from 1981. But only three months earlier they had scheduled a 7.3 percent increase. The next quarterly survey could well show an additional sharp drop, analysts said.

The business and personal income tax cuts at the heart of the Reagan program were supposed to encourage large increases in saving and investment. The resulting addition to the nation's productive capacity was expected to help hold down inflation in the future.

Now the outlook for investment is sufficiently gloomy that some top administration officials are questioning whether the president's program can achieve its long-term goals. Financing the huge prospective federal budget deficits will require a large share of the nation's total saving, saving that otherwise would be available to fund more business investment. At the same time, the size of the looming deficits combined with the Federal Reserve's tight monetary policies have kept interest rates unexpectedly high.

"If it takes 10 years to bring the fiscal equation back into balance, we will run such large deficits in the interim that we will never get the investment we want," one high administration official said in a recent interview.

The outlook is hardly bright for either deficits or interest rates. The Congressional Budget Office said yesterday that the Republican budget resolution passed by the House would produce deficits for the fiscal years 1983 to 1985 totaling $259.2 billion, more than $28 billion higher than its proponents claimed. The rejected Democratic version, which called for much larger tax increases, would have produced deficits totaling $248.5 billion over the same period, the CBO estimated.

Meanwhile, Treasury Secretary Donald T. Regan told reporters that passage of the Republican measure would mean that the commercial bank prime lending rate "will come down under 14 percent by the end of the year. If there is no budget at all, I don't see interest rates coming down."

Tbe Reagan administration predicted last year that the large business tax cuts approved by Congress would spur an investment boom. The bulk of the business tax cuts was tied to new investment, which now can be written off for tax purposes much more rapidly than in the past.

Not long after taking office, Regan told Congress the proposed tax cuts would cause business investment to rise 11 percent a year faster than inflation for at least the next five years. Investment would hit 12 percent of the gross national product by 1983--a level never before achieved by the U.S. economy. By 1986 14.4 percent of GNP would be invested by business.

Now the outlook is quite different. Even if there is a consumer-led economic recovery after the 10 percent cut in individual income taxes July 1, the Commerce Department survey indicates no increase in investment in the third quarter and only a 0.6 percent rate of increase in the fourth quarter.

Again, most private forecasts are more pessimistic. For instance, Data Resources, Inc., a widely used economic consulting firm, expects declining investment throughout the year, with the total, including farms, down 6.5 percent in real terms for the year as a whole.

If DRI's forecast for the next couple of years turned out to be correct, the share of GNP going for business investment during the four years of President Reagan's term would average about 10.8 percent, down from 11.2 percent during President Carter's four years in office. In addition, because of the deep recession, the level of investment will have been depressed substantially, not just the share of GNP.

Commerce Secretary Malcolm Baldrige, in a statement, compared the survey's 2.4 percent drop in real terms with an 11 percent decline in 1975. "The lesser decline in this recession is due to the accelerated depreciation portion of the president's economic recovery program," he argued. "Even though excess capacity is dampening expansion plans, businesses are buying machinery to increase productivity, reduce costs, and become more competitive."