Like Mark Twain, Israeli Prime Minister Menachem Begin thinks reports of his demise are premature. But his political obituary continues to appear almost daily in the Hebrew press, and a growing number of Israelis are talking about the next government as if early elections were a foregoing conclusion.

As often happens in Israeli politics, talk of a leadership crisis and the imminent collapse of the government reached near-frenzy levels last week and then just as suddenly vanished as a result of events not of Begins own making. This time that factor was an invitation by President Carter to meet in Washigton to give some momentum to the moribund West Bank-Gaza Strip autonomy negotiations.

As if an undeclared cease-fire on Begin had been made, the doomsayers of the prime minister's rightist Likud coalition put the subject of early elections on a back burner. They are perhaps mindful that Begin could adopt some of his opponents' positions in Washington talks -- as he did at the Camp David negotiations last year -- and return home triumphantly with a breakthrough impressive enough to carry him through the end of his first election term.

Also, some of Begin's critics in the coalition have concluded that it would be almost unpatriotic to bring the government down just two months before the May 26 deadline for the autonomy negotiations, and they have put into storage for the time being plans to force early elections.

But the underlying symptoms of the malaise of Begin's government not only continue to linger, but appear to be worsening.

Begin's personal popularity has plummeted in some polls to 17 percent -- compared to 57 percent a year ago -- and the Labor Party's standing has risen pro portionally. One survey by the Dahaf Research Institute shows that an election now would make Labor the first party to win an absolute parlimentary majority in Israel's 32-year history.

Inflation has risen from 35 percent a year when Begin took office in 1977 to a current rate of more than 140 percent, with no end in sight despite such desperation measures as converting the Israeli pound to the scaled-down shekel and withdrawing subsidies on many basic foodstuffs.

Begin increasingly finds himself in the minority in his own Cabinet and, as a result, has been hesitant to submit to a vote some controversial issues that would result in either a defeat or deeper division among the ministers. An example is the plan to place Jewish civilian settlers in the center of exclusively Arab Hebron in the West Bank, which is opposed by about half the 18 Cabinet members.

Moreover, the prime minister seems torn between making concessions to the ultranationalist settlement movement, the Gush Emunim, and bending somewhat to United States pressure to moderate Israel's policies in the occupied West Bank and Gaza Strip. The recent government decision to exporpriate 1,000 acres of Arab-owned land on the outskirts of Jerusalem -- and the subsequent international uproar -- only served to magnify the appearance of a government under siege from all sides.

In a heated Cabinet exchange recently, Defense Minister Ezer Weizman was reported to have said, "We can't go on like this. We're just making everyone sick of Israel."

Potentially the most dangerous threat to the Likud government, however, lies from within -- in the form of the National Religious Party, the pivotal coalition partner with 12 Knesset seats.

The titular head of the party, Interior Minister Yosef Burg, touched off last week's wave of early-election speculation by holding what seemed to be a highly suspicious meeting with opposition Labor Party leader Shimon Peres.

Coupled with the disclosure that Burg had ordered his ministry, which oversees elections, to begin printing ballots, the meeting shook some of Begin's Likud loyalists' faith in their leader's ability to survive until the scheduled elections in May 1981.

Under Israel's parlimentary system, a Knesset vote of no confidence in the government would force Begin to submit his resignation, after which President Yitzhak Navon would appoint a caretaker government -- traditionally the resigned government -- until new elections. Balloting could be held within 100 days.

However, Burg dampered rumors of an imminent collapse of the coalition by later denying he and Peres had been conspiring to bring down the government, and the National Religious Party's executive committee voted 10 to 2 not to discuss the possibility of a defection.

Some members of the party, however, are known to be afraid that if the Likud hangs on until the scheduled elecction next year, the Labor party will win such a decisive victory that it will not need a coalition partner.

These fears seem to ignore the long tradition of Labor-National Religious Party alliances and the fact that a victorious Labor Party would need it not only for a broader majority but for what some politicians call a "certificate of patriotism."

Peres has already hinted that even if the Labor Party wins an absolute majority, it would invite the National Religious Party to join its new government.

With the growing possiblity of early elections, talk has naturally turned to the makeup of the next government, an exercise that has been confused by the soaring popularity of Wiezman. While the Labor Party routinely crushes Weizman's Likud in public opinion polls the defense minister regularly comes out on top of Peres when voters are asked which man they would prefer to see as prime minister. In the most recent popularity poll, the charismatic Weizman was preferred over Peres 39 percent to 31 percent.

Predicting the members of a Labor Cabinet is further complicated by the death last month of former foreign minister Yigael Allon, who had just begun to mount a challenge to Peres for leadership of the party and the right to run for prime minister.

It is also clouded by the enmity between Peres, whose position at the top of the Labor Party ticket remains unassailable, and former prime minister Yitzhak Rabin, who said in his recently published memoirs that he would never serve in a Peres Cabinet.

Despite the bitterness Rabin retains against Peres, who as defense minister consistently undercut Rabin and weakened his leadership, incipent attempts are said to be under way for a rapproachement between the two rivals. Some of Allon's political allies are said to be actively involved in the peacemaking effort, arguing that it is essential to the success of the party in the next election.

It is widely assumed that if the effort succeeds, Rabin would be appointed defense minister, given his military background extending from being a commander of the under ground preindependence Palmach group and hero of the 1948 war to his role as the Army chief of staff in the victorious 1967 Six-Day War.

If Rabin instead were named foreign minister, given his diplomatic experience as Israel's ambassador to the United States and, later, as prime minister, former Army chief of staff Maim Bar-Ley proabably would get the defense portfolio.

The most likely candidate for foreign minister, apart from Rabin, is Abba Eban, the urbane and articulate former foreign minister and Israeli ambassador to the United States and the United Nations, who during the Labor governments was the most influential figure in Israel's relations with the West and world Jewry.

The crucial post of finance minister is likely to go either to Yaacov Levinson, chairman of Bank Hapoalim, the financial arm of the Histadrut (Israel's labor federation), or to Gad Yaccobi, former deputy minister of transport and a rising star in Labor before Likud came to power.

Levinson is the Wunderkind of the Israeli banking world, and could get the Ministry of Trade and Industry if the finance portfolio goes to somebody else. Yaccobi, a protege of Moshe Dayan, is chairman of the Knesset finance committee, but he recently underwent open heart surgery and his health may be a factor.

Dayan, who defected to the Likud Cabinet after a lifetime in the Labor Party, and then resigned as foreign minister last October, is not even a possibility in the next government. He has said he will not return to government service, and nobody has asked him.

There unquestionably will be battles in Labor in filling the top ministerial posts, and some of the principals are likely to be party leader Yossi Sarid, who reportedly is interested in the Foreign Ministry, Knesset member Aharon Yadln, former Labor Party secretary general, and Knesset member Ora Namir, a favorite for the Education Ministry.

If the National Religious Party joins the government, it is possible that Burg might return to the Cabinet, and that Education Minister Zevulin Hammer could get a post, although Hammer recently has become controversial as a hawkish supporter of Begin's aggressive settlement policy.

It is also, likely that the Ministry of Religious Affairs, tradtionally in the domain of the religious parties, would stay with the National Religious Party.