NEW YORK -- Here in the city with the world's largest Jewish population, where Yiddish expressions are part of the vernacular and Israel is seen by many as almost a sixth borough, the violent Palestinian protests that have shaken Israel for two months reverberate with special force. They have caused an emotional earthquake, more troubling even than the 1982 Israeli invasion of Lebanon, by raising prickly issues that cut to the core of Israel's identity and its reason for being.

"If Israel's policy is to beat people into submission, it's a mistaken policy," said Robert Lifton, 60, a Wall Street investor. "We as human beings have got to be very unhappy and uncomfortable about that policy. But what do you do when people are throwing rocks and Molotov cocktails at you?"

"It goes against everything we as Jews are taught," said Roberta Elliott, 38, features editor at Jewish Week magazine. "But the reality is they're in the Middle East, where an eye-for-an-eye and a tooth-for-a-tooth was invented."

"When we become like the enemy, then we are no different from the enemy," said Balfour Brickner, 61, a rabbi at a Manhattan synagogue. "It's painful to talk about it. When the ideals fade away and all that's left is the reality and the reality is ugly, what's happened to us?"

There are sharp differences of opinion among American Jews, a cross section of whom were interviewed here recently. But all are deeply concerned about the shootings and beatings of Arab civilians by Israeli soldiers, which have claimed at least 60 lives, and all are pessimistic about the prospects for peace. Some have taken a long, hard look into the mirror of Jewish nationalism and do not like what they see.

At the same time, most of those interviewed said they are fully aware of the complications and contradictions of the Middle East, of the intransigence on all sides, of the problems that appear to defy solution. Even as they decry the lengths to which Israel has gone to maintain order on the West Bank and Gaza Strip, they return again and again to the geopolitical realities that threaten Israel's survival.

It is as though they see Israel's existence as precariously balanced on the scales of American public opinion and, mindful of centuries of anti-Semitism, are afraid to tip those scales in the wrong direction. Most are not unsympathetic to Palestinian demands for greater autonomy, but worry how that would affect the security of an embattled country in which they have many friends and relatives.

The conflicting camps here mirror the divisions within Israel. Some make no apology for Israel's actions and view the Palestinian protests -- and the resulting deaths of some rock-throwing children and teen-agers -- as a cynical ploy.

"The Arab world has made the situation fester," said Judy Rosen, 36, a historian and Jewish activist in Forest Hills, Queens. "They're trying to play to the mercy of people by putting these little children out front. But a lot of these people are Arab fundamentalists and they have in mind that they're going to die as martyrs.

"You can't just say a soldier is out there shooting a child," Rosen said. "The Israelis have suffered so many casualties themselves. What are they supposed to do? Just stand there and let the Arabs run right over them and penetrate into their territories and kill women and children? They've had to do what they've had to do."

Others refuse to be drawn into the debate, saying that American Jews ought not to publicly criticize decisions made in Jerusalem and Tel Aviv.

"I, living in a Park Avenue co-op, do not have the right to make the determination what best assures Israel's security," said Rabbi David B. Kahane of Manhattan's Sutton Place Synagogue. "My son, studying for ordination in Efrat five minutes from the refugee camps -- he has the right to determine what best assures his security."

Brickner disagrees. "They don't have any trouble coming to me for money. When you get my money, you get my mouth."

Others try to tune out the troublesome questions, averting their eyes from news accounts that liken Israel to South Africa or describe the latest casualties. Even those who question Israel's policy of using fists to "strike fear" into Arab demonstrators, as Defense Minister Yitzhak Rabin put it, do so with obvious reluctance.

Jim Greilsheimer, 50, an attorney with Stroock & Stroock & Lavan, was hesitant to speak to a reporter about the recent violence. In a conference room at his Wall Street office, he protested that he was not an expert on the Middle East and had no "direct knowledge" of the pressures facing Israel.

When pressed, however, Greilsheimer spoke of his disappointment. "In the end, I think we expect much more from the Israelis than we do from other people," he said. "In the end, a policy of random beatings is counterproductive. The Israelis have to face the reality that the 900,000 or so Arabs who live in the West Bank and Gaza do not appear to want some type of annexation or affiliation with Israel, and therefore the policy of occupation is doomed to fail."

But Greilsheimer said of the Palestinians, "We're not dealing with people of good will . . . . We're dealing with people who I still believe seek the annihilation of Israel."

Roberta Elliott cares passionately about Israel but has little use for religion. She said she avoids synagogue "like the plague," but is immersed in Jewish culture and lived in Tel Aviv for four years before joining Jewish Week in 1985.

A former publicist for the National Symphony Orchestra in Washington, Elliott sees the Palestinian protests first and foremost as a news media story, saying the events are magnified by a huge foreign press corps that has placed Israel under a "microscope."

"The Palestinians have finally gotten smart," Elliott said. "I don't know why it took them 40 years to figure out how to get the attention of the world.

"When I see a bunch of Arab women on TV, screaming because their sons have been shot, I also know it's been staged just for the cameras. They know how many millions of people see the evening news in America every night."

But a moment after questioning the motives of the Palestinians and the press, Elliott assailed Israel in equally harsh language for the beating of civilians. She said she does not understand why tear gas and curfews are insufficient, and worries about the impact on young Israeli soldiers.

"We're talking about 18- and 19-year-olds, who are everyone's brothers, going in and beating the {expletive} out of another people," she said. "I'm wholly against it, no matter how much sense it may make to Rabin" and other Israeli leaders.

In her rapid-fire, New York style, Elliott ticked off a list of problems facing Israel -- a troubled economy distorted by huge military budgets, repeated clashes between orthodox and secular Jews, a political deadlock between leftist and rightist parties, and the ever-present Palestinian question.

To others, the Mideast picture is far more simple. Kahane, 58 -- a first cousin of Rabbi Meir Kahane, the extremist Israeli parliament member -- quotes passages from the Bible and his own sermons in defending the Jewish state.

"The world does not have to lecture the Jew on the ethic of nonviolence," he said. "The only time a Jew is allowed to engage in violence is in self-defense. The highest value in Judaism is survival. We have a mission to perform, and we can only perform that mission if we survive."

Like many of those interviewed, Kahane describes Israel as being "at war," a perpetual conflict that keeps shifting from the battlefield to the propaganda front. To those who criticize the reprisals against Arab demonstrators, he asked: "What is the counterproposal? Shall we bring them cake as a reward? This is the first time in history the victor is chasing the loser to sit down at a peace table."

Judy Rosen, who has visited Israel more than a dozen times, said that "Americans have a different perception of how life should be. In the Arab world, if there's someone somebody doesn't like, they knock them off. It's just beyond us to comprehend some of these things. We just come from a different civilization than the Arabs."

At the opposite ideological pole is Brickner, who heads the Stephen Wise Free Synagogue on Manhattan's Upper West Side. "I've been saying for 10 years that you can't treat the Arabs like this," he said. "You can't ignore the Palestinian problem. The Arabs have rights."

Brickner betrays the scars of years of internecine warfare in which he has argued that Israel must make greater concessions for peace. He said the Jewish establishment has castigated him and other critics as "radicals and crazies and self-haters and traitors."

But in recent weeks, Brickner said, disillusionment in the Jewish community here has become "more widespread than anyone dares admit. We invested ourselves psychologically, spiritually and intellectually because we believed Israel would be different than any other society. Then we begin to question what it is we've invested ourselves in."

Robert Lifton, who grew up in the Borough Park section of Brooklyn, where his parents were in the clothing business, now commands a spectacular view of the midtown skyline from his 32nd-floor office, where he is cochairman of the Marcade Group. He devotes considerable time to Jewish affairs and recently accompanied Jewish leaders on a trip to the Middle East.

Lifton said too many Americans view the recent uprisings as an isolated event, wrenched from the history of four wars that followed Israel's birth in 1948. The violence, he said, is a "symptom" of the fact that Israel, as an occupying power, has become mired in "cycles of repression and violence and repression."

"I watched one of those TV broadcasts showing Israelis beating Arabs and rapping a woman across the mouth," he said. "It was a terrible thing to see. But in this entire one hour, I did not hear anyone say the problem was that the Palestinians wanted the land the Israelis were on."

After a calm, measured analysis of the numerous obstacles to peace, Lifton's voice rose as he reached the brick wall that overshadows all discussions of Israel's future. The simple demographic fact that Arabs living under Israeli rule will soon outnumber Jews, he said, leaves Israel with a series of grim alternatives.

"You either incorporate the Arabs into the state and give them voting power, in which case you won't have a Jewish state. Or if you decide to keep them under some kind of control, then you don't have a democratic state. Or you expel them from the area, in which case you will be denounced.

"I think you must reach a decision that leaves you as a Jewish state and a democratic state, because that's what Israel stands for in the world. And that means giving up some territory for peace."

Many American Jews would challenge Lifton's conclusion, but few would dispute his contention that the status quo cannot be maintained indefinitely. And yet most of those interviewed see little hope for progress in the foreseeable future.

"There is a favorite Israeli expression, 'yeheyeh beseder,' which means 'Everything will be all right,' " Elliott said. "I don't think anyone believes anymore that everything will be all right. This is the end of the era of 'yeheyeh beseder.'"