THE CHAIRMAN of the House Budget Committee warned President Carter last week that the economy is sliding off the track that the administration has set for it. The chairman, Robert Giaimo of Connecticut, thinks that the President's economic forecasts are too optimistic - and that next year's budget deficit will be bigger than the White House expects. That's curious turnabout in the dialogue between Democratic Presidents and Congress. In the past, the Capitol has been the last place in town to hear public complaints about excessively optimistic budget predictions.

The key to this debate is business investment. It's been running markedly lower than is normal in the recovery from a recession. Both Mr. Giaimo and the administration consider this pattern of low investment to be a matter of profound concern. The question is what to do about it - and, to be candid, none of the answers so far sounds terribly convincing. The administration is urgently trying to reassure businessmen that the future atmosphere for profits will be good and inflation will be down. Budget deficits frighten businessmen, and that's why the President keeps reiterating his promises to achieve a balanced budget by 1981. The strategy is to create a climate in which businessmen will have the confidence to put more money into future growth.

The Democrats in Congress generally tend to take another view. They think, by and large, that business investment is a totally unemotional response to demand. A government's chief lever for raising demand is a budget deficit. A lot of congressional Democrats are deeply worried that, by locking himself into castiron commitments to eliminate those deficits, the President is foreclosing a vital instrument of policy. If demand drives the economy, and demand starts to go flat, what prospect does that leave for 1981?

This debate has been carried forward in rather muted ones. Mr. Giaimo's estimate fo next year's budget deficit, at $62.4 billion, is not spectacularly larger than the administration's $57.7 billion figure. The main reason for the difference is his expectation that economic growth will be slower than the White House predicts and will generate lower tax revenues. The President's economic goals can't be met, Mr. Giaimo said, "without a substantially larger increase in business investment than is now expected." That sentence is also a warning to other Democrats in Congress that it is now investment, above all, that counts.

The administration's views were set out explicitly earlier this month when Treasury Secretary Michael Blumenthal spoke in New York. If the country is to move toward full employment, he said, a larger share of our national output will have to go into productive investment. He's worried that American industry will again begin to bump against the limits of its production capacity, as it did in 1973. If that happens, he said, it will mean rising costs and further high unemployment. What's the administration's prescription to forestall it? Tax adjustments - and a lot of reassurance. Will that be sufficient? Nobody knows, but Mr. Giaimo doesn't seem to think so. If there is not a significant change in present inadequate investment rates by the end of summer, the administration will have to start looking for additional answers.