The first coup d',etat in U.S. history appears to have been accepted by the American people with surprising calm. There has been hardly any panic since the overthrow of the Reagan government, the stockmarket remains optimistic, and life seems to be going on pretty much as usual.

This unexpected equanimity in the face of unprecedented crisis may be attributed to the smoothness with which the coup was carried out, and also to the calmness with which the deposed leader himself has accepted his ouster.

Indeed, not even the most sophisticated Washington observers knew about the coup until former President Reagan revealed it during a nationally televised news conference last Thursday evening.

At an earlier news conference, this one on Sept. 29, the now-deposed leader was asked whether, in view of his "great distaste" for raising taxes, he could "assure the American people now that you will flatly rule out any tax increases, revenue enhancers or, specifically, an increase in the gasoline tax." The answer, more ominous in retrospect than was obvious at the time:

"Unless there's a palace coup and I'm overtaken or overthrown, no, I don't see the necessity for that."

Then last week, in an exchange with UPI's Helen Thomas, he revealed that the gasoline tax increase, which 43 days earlier had been "flatly" ruled out was under active consideration--even to the extent of renaming it a "user fee." That was the first official indication that, sometime between the Sept. 29 and the Nov. 11 conferences, there had been a "palace coup" or that Reagan had somehow been "overtaken or overthrown."

Edwin Newman and William Saffire, two of the country's best-known semanticists, have insisted that the original Reagan response should be read to mean only that he didn't "see the necessity for" flatly ruling out the tax increase absent a coup. However, most Washington observers, noting Reagan's frequently muddled syntax, assume that the former leader meant to indicate that a coup was imminent and that active consideration of a gasoline tax increase would be the cue that it had occurred.

Details of the apparent ouster are still not clear. Indeed, it is still not known who heads the new government. What is clear is that the change was handled with consummate grace, both by the coup leaders and by the former president himself.

Even the announcement was smoothly orchestrated, coming in apparent response to a routine question from a wire service reporter. But it can hardly be a coincidence that the revelation was made to the senior White House correspondent. There is some speculation that the entire exchange between Reagan and Thomas was pre- arranged so as to minimize public anic.

Early indications are that the coup was prompted by Reagan's refusal to take actions to combat the country's near-record and still-growing unemployment rate. The tax increase, which the former president earlier had refused to consider, would be used to finance repair of the nation's bridges and highways, both because they desperately need repairing and because it is a time-tested way of creating jobs.

Apparently, leaders of the new government have decided to let Reagan remain at the White House, as a sort of figurehead caretaker. The best explanation may lie in the national polls.

As matters appear to be unfolding, the American people will still have Reagan, whom they like personally, and be rid of his policies, which they found increasingly dismaying.

Such sensitivity augurs well for the future of America.