After three months of strong improvement, Americans learned to their dismay this week that the nation's trade deficit worsened sharply in June.

A single month's surge does not necessarily indicate a trend. Financial markets shrugged off the bad news, and economists said it was nothing to get alarmed about.So the Reagan administration isn't necessarily just whistling in the dark when it claims June's figures - the highest shortfall since last February - are only a temporary abberration.

Even so, it would be folly to ignore the message of this development and some of its possible portents for the future. Among other implications, the sudden and unexpectedly large surge in the trade deficit:

- Suggests that improvements in America's trade picture may very well come more slowly from now on, if they come at all.

- Provides new evidence that the economy is overheating, and that inflation may be harder to fight off.

- Shows that American consumers, including corporate buyers, still have a keen appetite for imported products.

- Raises the possibility that the surge in the trade deficit could eventually send the dollar into a tailspin and unsettle financial markets.

- Could influence the 1988 presidential election campaign. At this point, the new figures seem to dash George Bush's hopes that continued improvement would undercut Democratic efforts to make an issue out of the long deterioration in the nation's trade performance during the Reagan-Bush administration.

To put the June figures and the trade deficit in general in clear perspective, keep in mind that the trade deficit will be hard to reduce as long as the economy is expanding so rapidly that America consumes more than it currently is able to produce at home. When the economy does well, it naturally draws in imports.

Keep in mind, too, that - after adjusting for inflation - the U.S. trade deficit has shrunk by 43 percent since the third quarter of 1986.

But even after the most favorable interpretation has been applied, the fact remains that the day of reckoning can't be postponed indefinitely. America is still piling up debts to the rest of the world, debts that must eventually be repaid. The longer we wait, the more painful the task likely will be.