NOW IS AMERICA's moment in the Middle East," Alexander Haig said last May. Two weeks later Israel laid siege to Beirut and the American moment dissolved into a summer of White House impotence and frustration. Ariel Sharon's war in Lebanon has more to do with the Israeli-occupied West Bank than many observers at first realized. He calculated that a Palestine Liberation Organization defeated militarily and dispersed would no longer influence West Bank Palestinians to resist Menachem Begin's determination to keep the territory as an integral part of the land of Israel. The last thing Begin and Sharon wanted out of this war was what Ronald Reagan gave them September 1: a fresh U.S. peace proposal calling for Israeli relinquishment of the West Bank and association between the West Bank and Jordan. The president's plan faces awesome obstacles. Will he -- to borrow a phrase -- "stay the course" in the Middle East?

Seth Tillman says that all previous presidential peacemakers have failed because they have been unwilling to pressure Israel. The problem, he argues in The United States in the Middle East, is not that the Middle East is a complex place or that the competing stakes there are hard to reconcile. For Tillman these are secondary truths. Political constraints at home are the crux of the problem. The United States, he believes, must secure access to oil, must assure the security of Israel, must avoid Middle East war, and must be faithful to its historic commitment to the principle of self-determination. Yet presidents cannot pursue these four core national interests in proper proportion, Tillman writes, for one reason: "Owing to the unmatched influence of the Israel lobby in American politics, Israeli security (or, more exactly, the conceptions of Israeli security held by incumbent Israeli governments) has been permitted to preempt other vital interests in American policy." Tillman's prescription is for the United States to define a comprehensive settlement based on guaranteed 1967 borders, with Palestinian self-determination and to attach conditions to American military and economic aid to Israel, "which, if not accepted, would result in the United States government telling Israel: 'You are on your own.' "

In the debate about U.S. Middle East policy this prescription ceased to be novel a very long time ago. It has generated fierce polemics and a familiar litany of partisan argument. For a president or a Congress -- and Tillman was a senior staffer on Capitol Hill -- it ranks as one of the most sensitive foreign policy decisions that can be contemplated. It is therefore extremely puzzling that Tillman treats this volatile issue so cryptically, even casually, in a brief concluding chapter -- a few abstract propositions, but no discussion of practical politics, no hard analysis, no shading, no nuance. Carrots and sticks are available on many levels and in both directions in this dense bilateral relationship, raising as many questions about how the United States might bring influence to bear as about how Israel might resist. There is much to be said that is serious about this subject, pro and con -- all the more so since the events of last summer left the trajectory of U.S.-Israeli relations more uncertain than ever. Tillman, by settling for simple exhortation, has offered far less than what the coming American policy debate demands. In the end he seems convinced, but he is not convincing.

Of more immediate interest in Tillman's book, most of which is devoted to the 1970s, is his critical narrative history of American diplomacy during the Carter administration, his detailed look at Israel's occupation policies, and his ample picture of divergent U.S. and Israeli approaches to the question of Palestinian autonomy. No one reading this account will be surprised that Washington has decided Begin's version of autonomy is a dead-end or that the prime minister has flatly rejected the new Reagan plan.

Correctly, Tillman sees the contemporary Israeli- Palestinian conflict as an advanced stage of a historic clash between Palestinian and Jewish nationalism spanning much of this century. But to neither phenomenon does he do adequate justice. Palestinian nationalism is not, as he contends, a product mainly of the years since 1948. The formative years were the 1920s and 1930s, which are rich in meaning for the present day, explaining as they do both the fragmentation of Palestinian politics and the depth of Palestinian nationalistic fervor. In Tillman's portrayal of Zionism, Begin looms too large in historical terms, and mainstream Zionism, personified in Begin's bitter enemy David Ben-Gurion, recedes too far into the shadows. Though a towering figure today, Begin spent decades in the political and ideological wilderness. (Historians of Zionism and the Palestinian Arab national movement, incidentally, will be stunned by Tillman's linkage of Ben-Gurion, Chaim Weizmann, and Yasser Arafat as men who shared in theory a common vision of Palestine's future.)

While Tillman's confront-Israel message makes presidents acutely uncomfortable, Saadia Touval's history sobers them. In The Peace Brokers Touval, a political science professor at Tel Aviv University, asks the retrospective question: When has outside mediation failed or succeeded in the Middle East, and why? In rich, readable detail he chronicles three decades of failures and the few, by his reckoning, middling successes.

Mediators mediate, Touval says, out of self-interest -- defined, for the United States, as reducing Soviet influence, getting oil, maintaining preeminence. Mediators succeed not because they are impartial but because they have power. Bias may even help: Kissinger used to say that American mediation could work only if the Arabs saw Israel as a U.S. ally, and a stubborn one. The Arabs could get words and weapons from Moscow, but only through Washington could they get their territory back from Israel. Mediators court failure unless they bridle their ambition, unless they modestly work at the margins of what Touval calls "core values" affecting the "national self," and unless they realize that only the passage of time and the evolution of ideologies can resolve the conflict.

Here Touval is vague and unsatisfying, for he does not say exactly what core values are, who defines them, or what makes them change. A wrenching soul-searching is now under way in Israel about the nation's values. As for the Palestinians, which voice prevails? George Habash? Yasser Aafat? The mayor of Bethlehem? And were Anwar Sadat's core values different before and after his visits to Jerusalem?

Touval's perspective could serve either as a recipe for immobilism or as a prudent caution against extravagant hopes. It all depends. What is certain is that in the Israeli-Palestinian equation, everything touches gut issues that can no longer be avoided. Passage of time has not healed, it has only deepened the hatreds. Ronald Reagan and George Shultz have begun to face this terrible truth.