HAVING steadfastly urged voters to stay the course, the chief helmsman of the economy is now showing signs of panic. Worried that the recovery he has long promised isn't just over the next wave, President Reagan says he is thinking of asking Congress to accelerate the tax cuts now scheduled for next July.

Moving up the tax cut would give a quick boost to personal income. If consumers are in a buying mood, this should step up demand which, in turn, would give businessmen a reason to step up pro duction. It's the standard Keynesian response to a recession. It has worked reasonably well in the past. With the economy in the worst doldrums since the Great Depression, why not give it another go?

The case against this time-honored remedy rests on the fact that the economic world of the present is very different from that of the past. Even without the added tax cut, the federal budget will be running deficits next year and in the following years that are higher and more persistent than in any other post-World War II period. If deficits that big don't stimulate the economy, it is very doubtful that an additional $15 billion or so of added stimulus will have any noticeable positive effect.

If the accelerated tax cut doesn't offer much in the way of benefit, it certainly threatens considerable harm. The country has paid an enormous price in unemployment to get inflation down to its present level--which is still high by historical standards. The easing of inflation, as well as the depressed state of the economy has prompted the Federal Reserve to loosen up a bit on the money supply, and interest rates have fallen. These changes take a while to work their way through the economy, but if nothing upsets the current course of events, most economists expect a modest but sustained recovery to begin next year.

Any sudden change in signals -- such as the prospect of a stalemate over the budget or still bigger deficits in the offing -- could drive interest rates back up. That would mean more trouble for interest-sensitive domestic industries, such as autos and housing, and for exports as well. That's why Senate leaders and some members of Mr. Reagan's crew -- notably Martin Feldstein, chairman of the Council of Economic Advisers and David Stockman, director of the Office of Management and Budget -- are leery of a sudden change in signals.

The damaging boom-and-bust cycle of the last decade -- with each swing leaving both inflation and unemployment higher than they were before -- was made worse by the policy-makers' impatience. Remedial policies weren't given enough time to work before the government decided to try something else. In the changed environment of floating interest rates, hypersensitive investment markets and record deficits, there is even more uncertainty about whether particular policies will work. If recovery doesn't get under way next year, further course corrections may be needed. But a government that talks one day about the pressing need to narrow the deficit -- and the next day about new plans to increase it -- can only leave the country with the disquieting feeling that there is no one at the helm.