For decades American presidents faced with large budget deficits could confidently promise the nation that within a few years the red ink would disappear.

It never worked out that way in fact, but at least it looked true on paper: because of the progressive nature of the income tax, projected revenues always rose faster than projected spending.

Now it does not even look true on paper. Partly because of last year's large and continuing tax cuts, partly because of President Reagan's commitment to large future increases in defense spending, the spending trend line is rising faster than the revenue line, according to a wide range of budget experts, including some in the administration.

This fundamental change in the budget outlook cannot be altered by continuing to slash nondefense spending, the experts agree. Political resistance to additional major cuts is building, and even approval of another $30 billion worth of cuts, which Reagan is expected to seek this year, would reduce the deficit in later years but not come close to eliminating it.

The magnitude of Reagan's budget problem is almost unprecedented. Suppose, for instance, there is a moderate economic recovery this year that continues through 1983 and 1984. Suppose further that the president proposes and Congress agrees to raise excise taxes by $16.5 billion in 1984 and to cut nondefense spending by $53.6 billion from the levels called for by current laws. Finally, suppose that defense spending goes up only 4 percent or 5 percent faster than inflation between now and then, instead of the 7 percent rate the president favors. With exactly that set of assumptions, Data Resources Inc., the economic forecasting firm headed by Otto Eckstein, concludes that the 1984 budget deficit would still be $89 billion.

Analysts at the Congressional Budget Office have reached similar conclusions, as have some at the American Enterprise Institute and the Brookings Institution. Administration economists also agree privately that the lines charting revenue and spending growth in coming years will not come together without major fiscal policy changes.

Once defense outlays and interest payments on the national debt are set aside, there simply is not enough left to cut year after year to balance the budget without either more taxes or smaller defense spending increases, the experts declare.

The recession is swelling the 1982 budget deficit, which is likely to turn out to be close to $100 billion. But a brisk recovery will not eliminate deficits in future years. That is what has changed.

Meanwhile, recognition of this inexorable arithmetic by financial analysts is helping drive interest rates upward at the same time the economy is plunging ever deeper into recession. Industrial production fell 2.1 percent in December, matching the drop in May, 1980, when economists were saying the economy was in a "free fall." Over the course of the same month, some long-term interest rates rose more than a full percentage point.

These developments are causing some economists to question whether, in fact, there will be an economic recovery in the second half of the year. Economist Alan Greenspan, a regular adviser to Reagan, puts the odds for "no significant recovery" this year at 1 in 3.

Rudy Penner of the American Enterprise Institute, chief economist at the Office of Management and Budget in the Ford administration, fears that rising interest rates will choke off any recovery. And with a reference to the depressed economy of the United Kingdom, he declares, "The probability of Thatcherization of the U.S. economy has become very high."

Penner doesn't think financial markets will sit still for extended deliberations on how to effect a long-term solution to the new budget dilemma. He draws a parallel between the current situation and the winter of 1980, when interest rates shot upward after President Carter offered his fiscal 1981 budget. Within weeks, Carter was forced to proposed major spending cuts and to impose credit controls to try to calm the markets.

Penner believes that Reagan, like Carter, will soon "be forced into more vigorous action" than is likely to be seen in the 1983 budget Reagan will send to Congress on Feb. 8. Such action, as a practical matter, he adds, will have to come on the revenue side since the defense spending increases are not likely to be trimmed enough to make much difference. In any event, defense spending cuts would be unwise, in his opinion.

In a nutshell, one congressional budget analyst says, the problem is that last year's tax cut was so large that even with a healthy economy, revenues would be growing only about 7 percent a year while outlays, with the defense spending increases, would be going up about 8 percent to 10 percent annually. "It's quite a dramatic change," he says. "It really is. Suppose you cut nondefense spending by $30 billion. You've still got a growing deficit."

If there were no more nondefense spending cuts and no tax increases, the deficit could reach $200 billion by 1985, according to rough estimates by CBO.

Part of the reason for the long-run difficulties is that Congress pushed off until 1985 or later some of the larger revenue losses in the huge tax-cut bill it passed in August. The Joint Taxation Committee, which is in the process of raising some of its estimates, calculated the revenue loss from business and personal cuts at $150 billion in 1984, the year in which Reagan was then still committed to balance the budget. The revenue loss in 1985 jumps to $199 billion. Then in 1986 the loss jumps $68 billion. (None of these figures includes any "feedback effect" from added economic activity generated by the tax cuts.)

Beginning in 1985, the personal income tax will be indexed to the increase in consumer prices so that taxpayers will not be pushed into higher brackets by inflation. That provision will cost an estimated $36 billion in 1986 alone, the committee said.

Barry Bosworth of the Brookings Institution says flatly the 1981 tax cut was so large that "the president can never bring expenditures in line with revenues." For one thing, he notes, the size of the deficits themselves are adding to the following years' outlays for interest payments. A $100 billion deficit this fiscal year means, even at an average interest rate of 10 percent, $10 billion more in spending in 1983.

The $100 billion and $200 billion figures for the possible size of future deficits are so much larger than those Congress have found politically digestible in the past--even $80 billion or $90 billion has been out of the Capitol Hill ballpark in the past --that many members and observers doubt that it will be possible this year to get approval of a budget resolution. Realistic or not, members may refuse to put their names in an election year to something that suggests they approve of such deficits. Failure to pass a budget resolution could doom the entire congressional budget process.

There is no wide consensus among economists about the impact of continuing large deficits on the economy. Last week, Murray L. Weidenbaum, chairman of the Council of Economic Advisers, told an audience in Houston: "We cannot view substantial budget deficits with indifference . . . deficits do matter." (His emphasis.)

Financing the deficits absorbs credit that otherwise could be used by the private sector for investment and thus reduces the economy's long-term growth prospects, Weidenbaum said. "Financing the deficits makes the Federal Reserve's job of monetary restraint more difficult," he added.

Most economists would go at least that far in saying that deficits do matter. Assessing their impact on financial markets in the winter of 1982 is a much more uncertain business, but analysts such as Henry Kaufman of Salomon Brothers and Albert Wojnilower of First Boston Corp. believe that so long as mammoth deficits are in prospect a sustained economy recovery, and lower interest rates, are not possible.

On Friday AEI's Penner, Brookings' Bosworth and Lawrence Chimerine of Chase Econometrics all urged in congressional testimony that the personal income tax cuts scheduled for July, 1983, be postponed. "Tax cuts must be scaled back and new tax increases enacted," Chimerine said, otherwise interest rates will shoot back up.

The day before, Reagan, who still has not made up his mind whether to propose tax increases of the magnitude his advisers want, said in a New York speech, "If America can increase its savings rate by just 2 percentage points, we can add nearly $60 billion a year to our capital pool to fight high interest rates, finance new investments, new mortgages and new jobs."

He could have also added: the largest budget deficits in history.