The winner of the coming presidential election could find himself presiding over an economy that is turning sour, a growing number of economists say. ''The next president will have . . . a time with the economy and the deficit, '' says Walter W. Heller, chairman of the Council of Economic Advisers under Presidents Kennedy and Johnson and now an adviser to Democratic presidential hopeful Walter F. Mondale.
''There are problems building that make 1985 a question mark,'' adds James Pihera, assistant director of the Georgia State University Economic Forecasting Project. ''There is some doubt in my mind that we can get all the way through 1985 without some kind of downturn.''
According to the most recent monthly survey of major economic forecasters by Blue Chip Economic Indicators newsletter, most forecasters now expect key indicators - including economic growth, inflation, and unemployment - to be relatively well behaved through election day.
''Ronald Reagan is home free on the recovery and inflation,'' Mr. Heller admits.
The biggest preelection economic risk the President faces is interest rates. If they continue to rise, they could trigger additional erosion in the bond and stock markets. Such a turn of events could have a psychological effect on voters but would ''not cool off the economy that much in the next six months,'' says Robert Wescott, senior economist at Wharton Econometric Forecasting Associates.
But by 1985 a pronounced slowing could be taking place in the economy, forecasters say, as companies are no longer able to fund investments in new plant and equipment out of profits. Demand for capital from increased private borrowing would then run headlong into demand from the federal government trying to finance a $200 billion deficit. Economists say they expect that the fiscal 1985 segment of the deficit will be trimmed only slightly or not at all by Congress before calender year 1985 is well under way.
The result, the scenario goes, will be rising interest rates that, at best, slow economic growth to a crawl and at worst plunge the economy into a recession. The prospect of rising interest rates and sagging economic growth finally will force Congress to make major deficit reductions, these experts say.
''Everything is building to a crescendo of higher interest rates toward the end of 1984,'' says Edward Friedman, senior economist at Chase Econometrics, another forecasting firm. He says he expects that rates will rise between two and four percentage points from the end of 1984 through the first six months of 1985.
''That is enough to drive the economy at the very least into a significant deceleration,'' he says.
And a recession could result, Mr. Friedman warns, unless Congress makes major cuts in the deficit in 1985, which would allow the Federal Reserve Board to loosen credit conditions and help lower interest rates.
The deficit trimming packages being debated this week in the House of Representatives envision relatively small deficit reductions in fiscal year 1985 , forecasters note.
''The numbers are very small in the context'' of the problem, Mr. Wescot says. For example, the Reagan administration's proposed $149 billion, three-year reduction package is designed to trim $26 billion in fiscal year 1985. And many economists say that, due to budget estimating problems, the actual reduction would be smaller than that. Fed Chairman Paul A. Volcker has told Congress it takes a $50 billion deficit reduction to trim interest rates 1 percentage point.
The expected slowdown could limit new political initiatives, either by a reelected President Reagan or a victorious Democrat, because federal tax receipts decline when the economy cools off.
In fact, the slowing economy may make it especially difficult for Congress to trim the deficit because cutting federal spending tends to deepen a recession.
''That is the biggest risk'' of Congress's failing to take major deficit cutting action now, says Robert Gough, senior vice-president of Data Resources Inc. ''The economy could tie their hands in 1985 if they don't act now.''
Most forecasters do not think rising interest rates will trigger rampant inflation.
''Volcker is not going to lose that which he already has gained'' in the battle against inflation, Mr. Gough says. ''He is not going to sit back and let inflation move to 7.5 percent, 8 percent, or 9 percent.''
If inflation started to accelerate, Gough says he thinks the Fed would clamp down on the economy further. But economists say they expect inflation, as measured by the consumer price index, to pick up speed throughout 1984 and '85 and end '85 at 6.5 percent.
It is well to remember that forecasters are not always right. The economy might avoid the expected slump if Congress were to slash the deficit by a larger-than-expected amount before the end of 1984 or very early in '85, forecasters admit. But this scenario is not seen as likely.