Although constitutionally and from a procedural point of view it is easier and quicker to topple an Israeli prime minister than to remove a president from the White House, it is nevertheless, in principle, a process that requires a majority. At this point, Prime Minister Menachem Begin has the majority both in the Knesset (parliament) and in the polls (if elections were held today) to stay in power. But there are forces at work that have just started to gather momentum, and if this continues, a change of government seems inevitable.

Under growing political, public and press pressure, Begin had to agree to appoint a special investigator to look into Israeli conduct before, during and after the massacre at two Beirut Palestinian refugee camps. He had to do so after he exhausted almost every political trick in his seemingly bottomless hat to persuade his coalition partners to wait at least two weeks before doing just that.

The special investigator he turned to is the president of Israel's Supreme Court, Chief Justice Yitzhak Kahan. But the justice declined to either accept or reject the appointment as long as the court did not rule on a pending matter: a demand by some groups and individuals that the court should order the government to establish an official committee of inquiry. Thus, the justice has practically negated one political advantage Begin had hoped to win from his hasty turnabout -- to defuse the impact and the enthusiasm of the largest anti-government rally in Israel's history the following day (yesterday).

This in itself is a major political setback for Begin and his beleaguered government. It may turn out to be even worse if the Supreme Court, in ruling on the matter before it, merely hints that an official committee seems more appropriate under the prevailing circumstances.

Begin had already lost the support of one of his ministers, Energy Secretary Yitzhak Berman, and of another Knesset member of his own Likud party over his failure to appoint an official committee of inquiry. The government parliamentary majority stands now at 62 out 120. The opposition Labor alignment has 50 votes and can always count on the support of two Shinui party deputies. It can also always count on the four pro-PLO Communist members of the Knesset to vote against Begin. But Labor would be ill-advised to form a government that would depend in any way on the good will and votes of the Communists, who are vocally anti-Zionist and seen by many as almost traitors.

Mathematically, the situation is simple: 62 support the government; 56 oppose it; and the two Likud "deserters" would oppose it on any issue relating to the war in Lebanon, the continued presence of Ariel Sharon as defense minister or the investigation of the massacre by anything less than a full-fledged official committee of inquiry.

But there is more than mere arithmetic here. The coalition consists of members of six different factions in the Knesset (Likud is the largest with 48 officially, but 46 effectively). Of the other 18 deputies who support the government, at least 10 are on record as favoring an official committee of inquiry. They have agreed very hesitantly to the appointment of a special investigator. Most of the 10 represent religious parties that find it impossible to play politics with such an explosive and delicate moral question.

This in itself is a precedent in Israeli politics, for until now religious parties behaved just like any other political body. Begin's only trump card in dealing with his coalition partners is to threaten to call an election. He knows--and they understand -- that in such an event some of them would be wiped off the Israeli political scene. But as the education minister, Zvulun Hammer, whose party is the most vulnerable in an election now, told his party: "We have reached a watershed. We are not trash. On this issue I amready to face the voters. I will not serve in this cabinet if this terrible tragedy will not be totally and thoroughly investigated."

Another of the 10 is minister-without-portfolio Mordechai Ben-Porat--a close ally and admirer of the late Moshe Dayan. Ben-Porat was the first to demand, in a private letter to Begin, a full-fledged inquiry. Ben-Porat will never forget that his leader, Dayan, was undone by a similar inquiry following the Yom Kippur War. So on top of his deep belief that such an investigation is obligatory, Ben-Porat also secretly wants to redeem Dayan's memory.

Three more of the pivotal 10 belong to the Tami faction, essentially an ethnic political entity, with strong religious overtones, to whose flag rallied many of the disenchanted members of the non-Western intelligentsia, Jews whose origins are mostly in Mideastern counties. They are both morally outraged at what happened in Beirut and politically frustrated at their scant influence on Begin's social policies. In addition, they bear a grudge against Israeli society because their leader, Aharon Abu-Hatzeira, was convicted earlier in the year on charges of mismanaging public money. He had to resign his cabinet post, and now he waits for the Supreme Court to rule on his appeal.

Abu-Hatzeira is very close to former defense minister Ezer Weizman, who broke ranks with Begin more than two years ago. Since then, Weizman has kept himself occupied in business and in deliberate and concerted efforts to create or to seize an opportunity to return to active political life. Publicly Weizman has kept quiet, but privately he tells anyone willing to listen that he is horrified at the way the country is being led. He fears for the future of Israel.

It is Weizman who has now become the center of attention. Many political observers and professionals believe he can become the focus and leader of a new political force that could have enough support to effect a change of government. Weizman is still quiet, examining his options and planning his strategy. He lives in the small settlement of Caesaria, which appears more and more to resemble the little French village of Colombey-les-Deux-Eglises from which Gen. Charles de Gaulle reemerged in 1958 to change the fate of France. Weizman could conceivably persuade two or three more deputies to desert Likud. Together with the three Tami deputies and the "deserters," he could lead a parliamentary bloc that would provide Labor with the margin necessary to replace Begin's Likud government.

In a rare occurrence, the mass circulation evening newspaper Yediot Achronot prominently printed Friday an editorial by its publisher titled "Ezer Now." It calls for the immediate invitation of Weizman into a new cabinet of national salvation.

Inside Likud itself, things are not calm either. A number of ministers believe Begin erred in refusing to appoint an official commission of inquiry. Others feel they are paying dearly for the presence among them of as controversial a figure as Ariel Sharon. The defense minister is the most brutal political force ever to hit Israel. He is a political hurricane, a man of little regard for procedure and legalities, a second-to-none field commander with seemingly unlimited energy and perseverance.

"He does what he wants," says a close aide. "If they will not let him do it now, he will find a way later."

"He is one of a kind," says an admiring friend. "When he decides to do something, there is no way to stop him and it will either be a tremendous success or untold disaster. There is no in-between for him."

But Sharon's greatest liability, and it reflects very badly on Likud, is the widespread belief in Israel (not necessarily substantiated) that he is immoral and a liar.

Israel is in the midst of a moral crisis. The massacre in Beirut is a challenge to the country's raison d'.etre. In such a crisis, the last thing the country needs is a defense minister whose moral credentials are, at best, widely doubted. The energy secretary, in an interview after his resignation, accused Sharon of executing two of the four crucial moves during the Lebanon war without prior approval by the entire cabinet. He referred to the Israel incursions into East Beirut in June and into West Beirut 10 days ago. One of the reasons Begin did not want an inquiry into the massacre is probably his fear that it may expose the poor procedures by which this entire war was conducted.

But the outrage in the country appears unstoppable. Feelings of guilt are overflowing. The belief of many is that Israel is morally responsible for the massacre by the mere fact of its troops' being present nearby and because of the gross misjudgment in allowing the murderous Christian militias into the camps. It is just as bad as letting armed Palestinian terrorists into a Christian neighborhood. There would have been a similar slaughter.

There is widespread belief here -- which I share wholeheartedly -- that this moral responsibility is absolute, total and forever, no matter what an inquiry may conclude. Our personal and collective national conscience will forever trouble us. What happened in Beirut was almost as bad as a pogrom. Pogrom is the second most dreadful word in the Jewish vocabulary. The first is holocaust.

Against this background, the imponderables and the unusual among the forces that are at work become more important, probably decisive. The rules of the political game and its arithmetic are much less relevant. For the first time, the most sacred cow of Israel -- the military -- is sacred no more. It has been heavily criticized in the past, but never as profoundly as it is now. Israeli public opinion has been outraged before, but never by such horror and never because of fear that Israel's basic absolute moral justice has been undermined. Israel's press, always vigorous and combative, has never been so eager to expose every facet of the catastrophe with so little regard for security considerations. For the first time, Israel is undergoing a soul surgery, and the country is committed to see it through, believing it will emerge from it stronger and more just.

Politically speaking, all those who can possibly oppose Begin had already joined the opposition long before the war in Lebanon started. But now a sizable number of people who support him and most of his policies, including the decision to go into Lebanon and even the conduct of the war, are making their disappointment known. The turning point was his refusal to appoint immediately a commission of inquiry.

The most potent factor at work is the criticism inside the military. This has reached unprecedented levels. Privates and other low- ranking soldiers talk about it almost freely. Despite censorship and other restrictions -- both utterly justified -- what they say reaches the civilians. It crops up in newspaper reports and in private social discussions.

Most threatening is the new manifestation of high-ranking officers either resigning or asking for a leave of absence. One colonel, Elie Geva, a bright and promising tank brigade commander, resigned his post, anticipating that an order would be given to attack West Beirut and that he would be unable to obey it. Soldiers are now openly criticizing Israel's presence in and around Beirut. In their simple ways, they state: "It is none of our bloody business."

Last week, a leading young general, Amram Mitzna, commander of the army's staff and command school, asked the chief of staff to be relieved of his duty. He is reported to have told his superiors he cannot serve as long as Sharon remains the defense minister. Reports are circulating that other high-ranking officers are considering similar actions but are waiting to see how the question of the inquiry is resolved.

When all these forces converge, even a weathered politician, a truly charismatic leader who is genuinely and sincerely devoted to his people, as Menachem Begin no doubt is, will survive onlyens by miracles.