Jerusalem — Resignation of Finance Minister Yigael Hurwitz has left Israel's government in its weakest state since assuming office nearly four years ago -- and has reduced its staying power to the barest minimum.
Ostensibly, the hard-nosed economic czar stepped down Jan. 11 in a Cabinet dispute over teachers' salary increases. He refused to bow to an 11-to-3 Cabinet majority that favored costly improvements in the working conditions of Israeli educators.
But Mr. Hurwitz's real motive may well have been to separate himself and his small but pivotal RAFI party from the fading fortunes of Prime Minister Menachem Begin's right-wing Likud coalition government.
As of this writing, it was up to Mr. Begin himself to decide whether he can and should continue in office despite the Hurwitz defection. If the decides to stay, his government will have to rely on maverick Knesset (parliament) deputies to muster parliamentary majorities whenever challenged by votes to confidence. Alternatively, he could decide to step down immediately after the Hurwitz resignation takes effect on Jan. 13.
The two-day interval is required under the rules of Israel's parliamentary game. It will enable Mr. Begin to remain at the helm in caretaker status without having to keep a finance minister in the Cabinet against his will.
The situation would apply were Mr. Begin to tender his own resignation to President Yitzhak Navon, opening th way for legislation to authorize a national election within 100 days instead of in November, as normally required by law.
In either case, Israel will be under the direction of a leader bereft of the political mandate and moral authority necessary to make crucial decisions, especially in the sphere of foreign policy.
It means that President-elect Ronald Reagan and his incoming team of United States policymakers may find it difficult to gauge Israel's responses to new initiatives regarding the Palestinians or the various Arab states.
The issues facing Mr. Begin's government, whether it lasts a few days or until November, would challenge even the strongest of national leaders. Included are:
* Egyptian and American interest in diplomatic headway toward a viable proposal for Palestinian autonomy in the occupied Jordan West Bank and Gaza Strip, as required in the Egypt-Israel peace treaty.
* A dangerous military threat from the Syrian armed forces deployed on the fringes of the Palestinian guerrilla foot- hold in south-central Lebanon (due to Syria's refusal to let Israel's anti-guerrilla forays and air strikes go unchecked).
* The Western world's highest rate of inflation, soaring toward the 200 percent mark.
* Declining Jewish immigration, including a dip in the number of Soviet Jews opting for Israel rather than the US and an increase in the number of Israeli citizens emigrating to the US, South Africa, and other economically promising lands.
* Embittered young couples and financially strained families unable to mobilize the astronomical sums necessary to purchase decent living quarters.
Israelis looking for a strong hand in the incumbent Likud regime may find it in Agriculture Minister Ariel Sharon, who advocates massive Jewish settlement of the areas under military rule.