The joke making the rounds of the Israeli parliament dining room these days is that Prime Minister Menachem Begin doesn't really have a problem with what to do about the future of the West Bank and the Gaza Strip. All he had to do is say "yes" to President Carter and make it sound like "no" to the Israelis, or say "no" to Carter and make it sound like "yes" to the Israelis.

Underlying the facetiousness of those choices, however, is a crisis in government that Israeli political leaders who have been active since the founding of Israel say has rarely been matched before.

It is a crisis of complex dimensions, involving nuances hidden deep among the whereases and wherefores of the Israeli Cabinet ministers' various draft proposals for the future of Arab self-determination in the territories occupied during the 1967 Six-Day War.

But, in the end, it finally gets down to the gut issue that the Carter administration was trying to get at when it presented Israeli Foreign Minister Moshe Dayan in April with a set of two diplomatically phrased questions: Is a final settlement of the sovereignty issue in the West Bank and Gaza possible after five years of proposed limited self-rule? How will the Palestinian Arabs achieve a measure of political self-expression at the end of that time?

Behind those questions lies the broader and more troubling questions that is at the root of the divisiveness in the government, but is rarely mentioned so starkly in the utterances of public officials. Is Israel going to give up it s historical attachment to the biblical lands of Judea and Samaria, forever, and if so, when and how much of that will it relinquish.

Recriminations are beginning to pop up, with members of the Herut faction of Begin's conservative likud coalition accusing Dayan of getting the Cabinet into this mess in the first place by even agreeing to accept the United States questions.

Begin was reported to have threatened to quit if his Cabinet fails to honor his insistence that the government not commit itself to discussion of the final status of the occupied teritories. he is said to have told colleagues that he would consider a Cabinet vote against him a personal matter.

The primitive instinct of political survival also is beginning to surface, with reports that Labor Party and National Religious Party leaders have been meeting secretly to discuss a possible coalition just in case Begin's Likud coalition crumble sin the current crisis.

No matter what compromises are reached in upcoming Cabinet meetings, the problem Begin Had before of avoiding an alienation of Washington has changed in the last week into a problem of how to aavoid an irreconciliable alienation within his own government.

Begin, in defending the hard-line position of committing Israel to as little as possible until ehe end of the five-year expdriment in limited Arab self-rule in territories, has become a minority in his own Cabinet.

The irony of that situation is clear. The Likud Party ascended to power a year ago in part because of Begin's appeal to the nationalistic grain that runs so deep among Israelis, and his unequivocal stand against giving in to the Arabs' demands for territorial concessions. It was Begin and those sharing his ideology who resisted Israel's first partition plan seeking more territory, and he was remembered in the last election for promising not to give in to the yielding of land that Israelis believe to be historically theirs.

None of the 19 Cabinet ministers has publicly sovereignty in the West Bank and Gaza. nor to relinquish the right to defensible borders nor the right to maintain settlements in the areas.

But the three major plans put forward so far for the future of the territories after five years offer a semblacne of flexibility in degrees.

The most conservative one is posed by Minister Without Portfolio Chaik Landau, who avoids any mention of a "final" status for the areas but proposes that at the end of five years Israel will make up its mind on the basis of the experience during the trial period.

Dayan's plan, which includes an active role for Jordan in the autonomy period, alluded to a permanent status for the inhabitants of the territories after the five years. It also includes a number of safeguards, including Israeli military presence after five years, the right for Jews to settle in the West Bank and the exclusion of a Palestinian state in the areas.

A proposal by Defense Minister Exer Weizman stresses open negotiotions with Egypt during the five years, and leaves open to talks such crucial points as settlements as settlements and soverignty.