Last week there was joy in the Great Republic, and by the week's end it was dawning on a lot of Yanks that Ronald Reagan had already accomplished considerable good. He had brought dignity to realms where there recently had been mawkishness and botchery. He had convincingly suggested that America again has a serious government run by serious men.

Yet buried in all that elation was an ominous news story, which deserves to be disinterred and faced squarely. There are mice (peromyscus leucopus ) in the White House. More distressing still, these mice were in residence there during the previous administration, and Jimmy Carter was powerless to effect their departure. Notwithstanding the fact that, as president, Carter was commander in chief of the entire armed might of the United States and still very influential with the NATO powers, the mice remained. This might strike some as a very insignificant matter, but here they would be in error. The saga of the White House mice is but another sign of the feeble voltage of presidential power nowadays.

Let me not be misconstrued by my fellow liberals. I am not desirous of a return to the Imperial Presidency. But I do think we should face up to the fact that recent developments have rendered the presidency far less forceful than the Founding Fathers intended or than modern times demand. We must have an effective chief executive. Is the thing possible?

It is not as though President Carter had been indecisive about these mice.

From all the evidence that I have been able to gather, here was Carter at his best. He was thoughtful, tough and resolute. He understood the potential danger of having mice in the Oval Office, especially in the Age of Television. He analyzed his alternatives, calculated the costs and ordered extermination. Nothing happened. Such is the bureaucratic miasma now surrounding the office of the presidency that the order simply expired, a casualty of bureaucratic infighting and the president's inability to bend the government to his will.

No department would act on the president's order. The Department of the Interior pointed to the General Services Administration. GSA denied that it had authority to undertake the grisly task and pointed back to the Department of the Interior. The mice continued to frolic and to scamper in the shadows of the high and mighty.

Will the Reagan administration manage to be any more forceful with the bureaucracy than its predecessor? I have my doubts. Last week I telephoned Peter McCoy, Mrs. Reagan's chief of staff, and asked him what he intended to do about the White House mice. He was understandably cautious, pointing out that at this point he had seen only "mousetraps" on the premises. When I informed him that Carter had found mice in the Oval Office, McCoy assumed a triumphal tone, assuring me that once the mice were discovered they would be "exterminated."

This is just the reply one might have expected from the inexperienced lieutenants of a new administration. If only the world were so simple. McCoy knew nothing of the past administration's troubles and became decidedly impatient when I tried to enlighten him. Nor did he seem to be aware of the political costs inherent in his bold plan. Exterminate them? Not only is the presidency bound up by bureaucratic pussyfooters but there is a multitude of political pressure groups now, each one capable of scotching a presidential initiative. Before McCoy and his associates blithely enter upon rodenticide, I suggest that they consider the work of Michael W. Fox, scientist and humanitarian.

Fox, author of "Understanding Your Dog" and numerous other thoughtful tomes, is one of the leading advocates of animal rights in the world. He is not to be taken lightly. There are thousands, perhaps millions, like him, and I doubt that they will sit sweetly by while the new occupants of democracy's mansion fall upon harmless creatures whose residency there might trace back through generations, much as the cats (felis domestica ) disporting in the Roman Forum today trace back to the times of emperors.

In his latest book, "Returning to Eden: Animal Rights and Human Responsibility," Fox gives us a sense of what the new administration will be up against if it comes down hard on the White House mice. "Human liberation will begin when we understand that our evolution and fulfillment are contingent on the recognition of animal rights and on a compassionate and responsible stewardship of nature. The dawning of a new Eden is to come." Peter McCoy and his exterminators had best tread softly.

President Reagan is off to a good start. Yet he has a very difficult road ahead. The saga of the White House mice suggests that he will need more than wise counsel. He will need a staff capable and willing to do what is necessary to turn his decisions into government policy.