Jerusalem — The political future of Prime Minister Menachem Begin is a major subject of local and foreign speculation as he returns to work after a one-week mourning period for his late wife, Aliza.
The problems facing him are substantial, ranging from the inquiry into the Beirut massacre of Palestinians to a sagging economy to the growing difficulties of extricating Israeli troops from Lebanon.
But a consensus is emerging here among pollsters, political analysts, and politicians that - barring an unforeseen crisis - the odds are high that Mr. Begin and his government will remain in power.
''This government could be named after the television series 'The Untouchables,' '' wrote respected political analyst Yoel Marcus in the independent daily Haaretz. ''Many times it nearly fell but it still goes on standing.''
Speculation on Mr. Begin's difficulties has focused on two main themes: the personal impact on the prime minister of his wife's passing; and the potential impact if the inquiry commission should hold the government or any minister responsible for the Beirut massacre. In the wake of the Beirut massacre there were hints within the ruling coalition that some small but key partners might jump ship to form a new majority coalition with the Labor Party.
[Reuters reports that the commission has announced that Mr. Begin and eight others might be harmed by its findings. In the most explosive development since the judicial inquiry began five weeks ago, the commission advised the nine that they had the right to testify again or take legal advice.]
On his personal future, only the prime minister can give the definitive answer. But sources close to him say he does not intend to retire or resign.
''He wants to stay in power to finish his historic mission - to guarantee that there is no partition of Eretz Israel [Israel and the occupied West Bank], '' said one source.
As for the commission's results, several analysts from both Likud and opposition camps predicted, in the words of one, that ''unless there is something dramatic connected (by the commission) personally to Begin's name'' he will not step down. The evidence revealed so far in public contains no such bombshell, they believe.
Moreover, the commission's findings are not binding, so the government is not legally required to dismiss anyone who may be censured.
''If there is some general criticism against the government, would it fire itself?'' asked Likud Knesset (parliament) member Ehud Olmert, rhetorically. His answer: ''No.''
But some opposition members have been basing their hopes on the precedent of the Agranat Commission set up in 1973 to investigate Israeli military unpreparedness for the 1973 October War with neighboring Arab states. The Agranat Commission called only for dismissal of military and intelligence chiefs , but the ensuing public uproar brought down the Labor Party government of Prime Minister Golda Meir.
However, commentators have pointed out that the Agranat Commission was investigating a subject that uniformly shocked the Israeli public: the unnecessary deaths of thousands of Israeli soldiers. In contrast, wrote Haaretz's Mr. Marcus harshly, ''Sabra-Shatila [where only Arabs died] doesn't shock them or is pretty popular.''
Prime Minister Begin's substantial popularity, which dipped just after the massacre, appears again to be on the rise, according to recent polls. By early November a Jerusalem Post poll conducted by the Modiin Ezrachi Research Institute, which had showed a dip from 49.8 percent just before the massacre to 42.9 percent just after, found that 44.8 percent of the population considered Begin best suited for the prime minister's job. The remaining percentages were scattered among other names and the undecided.
Less certain, believe observers here, is the fate of Defense Minister Ariel Sharon, whose personal popularity has dipped sharply since the massacre, according to the poll. Some analysts think there would be a public outcry from Likud supporters if the military were blamed for the massacre and Mr. Sharon were spared. ''[Chief of Staff Rafael] Eitan is seen as clean and Sharon not,'' says Nahum Barnea, editor of the new weekly magazine ''Headline.'' Other analysts predict that Mr. Begin might keep his defense minister, even if he were compromised, and ease him out later on.
In any event, most pundits do not belive the demise of Mr. Sharon would mean the resignation of Mr. Begin. The prime minister has a pressing parliamentary reason for refusing to step down. In the Israeli system only the parliament can dissolve itself, by majority vote. Although Mr. Begin personally favors new elections before his mandate expires at the end of 1985 - polls show Likud is out in front of Labor - his Likud coalition with 46 seats does not command a majority. The Likud's small coalition partners, notably the National Religious Party and Tami, are leery of early elections that might reduce their seats.
But should Mr. Begin step down there would not automatically be new elections. President Yitzhak Navon would be required to ask the head of the largest parliamentary faction to form a government. The largest faction is the opposition Labor Party with 50 seats, headed by Shimon Peres. Thus Labor could be handed the chance to form a government without new elections. (Even in this case, should the Likud inform President Navon that they could form a new coalition majority under another leader, they could still hold onto the government.)
Should Labor take power by a parliamentary maneuver, many observers think the government would be hampered by the resentment of the massive Likud followers.
''It would be doomed to complete paralysis and a very short life which would end in elections that would return the Likud to power,'' speculates analyst Marcus.
However, if Mr. Begin stays in power, observers doubt any of his coalition partners will bolt - in large part because of the disarray of the opposition. Labor has been so ridden by internal dissent and leadership struggles that it has been unable to capitalize on Mr. Begin's problems.
The government handily defeated 59 to 50 a Labor Party motion of no confidence on Wednesday over the New York Times report that opposition leaders favored American aid cuts to Israel in order to bring down the Israeli government. Likud leaders used the Times story to hang a ''traitor'' label on Labor Party leader Peres, although the Times report named no sources.
''The Likud, especially Begin, have permanently made a demonization of Peres' personality among the Israeli public,'' complained Labor Knesset member Shevach Weiss. But in a telling illustration of Labor's destructive internal squabbling, former premier Yitzhak Rabin, who wants the party leadership back, argued publicly with Mr. Peres over whether the no-confidence motion was ill advised.
''If Begin is not found guilty (by the commission) and if he retains the motivation and strength to stay in the center of the Likud, then I think he can overcome his other problems,'' said one Labor Party member gloomily.