LAST OCT. 8, Israel's new prime minister, Shimon Peres, arrived in Washington asking for U.S. help to deal with the most dangerous problem to face the Jewish state since the 1973 war. That problem this time was not a military threat from the Arabs, but an economic hemorrhage threatening Israel's stability.

Peres, who had taken office less than a month earlier, arrived with a request in his pocket for $1.5 billion in U.S emergency funds to be added to already-planned aid totaling $5.6 billion over two years. The total sum of $7.1 billion over two years -- none of which has to be repaid -- would amount to about $1,650 from American taxpayers for each of Israel's 4.3 million citizens. These grants amount to one of the largest aid programs in modern history.

The Reagan administration, which has been strongly supportive of Israel, did not balk at the size of the increase. But led by Secretary of State George P. Shultz, the administration insisted that the extra aid be accompanied by "meaningful" economic reforms to repair Israel's fundamental problems so that the money would have more than fleeting effect.

In the eight months since Peres' visit, Washington and Jerusalem have engaged in highly unusual and sensitive bargaining over the Israeli economic policies. Although theoretically the United States held all the cards, it has not worked out that way in fact. As of today, as a result of extraordinary political influence with Congress, Israel has been assured of getting its emergency U.S. aid. The United States, however, is far from assured that Israel in return will take the strong measures that American and Israeli experts believe are needed to deal with Israel's underlying economic problems.

As a result, the United States' aid program to Israel is entering a high-risk phase -- for both countries -- during which the Jewish state may either correct its economic problems and move toward greater financial independence or fail to take decisive steps and wind up dependent on American aid at a higher level than ever. And if the Israeli reform effort fails, American disillusionment could make another U.S. rescue effort extremely difficult.

The story of the aid-and-economy discussions since last fall is an illuminating chapter in how the unprecedented intimacy between the United States and Israel works these days. It is also the story of a particular passion of George Shultz, whose eyes light up with interest when discussing economics, a subject that puts most top officials in Washington to sleep. Shultz's views on the Middle East have swung notably toward Israel in three years as secretary of state. He saw a great opportunity, an aide said late last year, to make a lasting contribution as the world statesman who saved the Jewish state from economic ruin. In effect, Shultz undertook to play the role for Israel that the International Monetary Fund plays for most economically- troubled nations -- providing emergency funds in exchange for austerity and reforms.

Shultz's efforts to help Israel help itself were frustrated in part by the eagerness of Congress to extend aid -- reforms or no. In recent years, Israel has mastered the congressional process, aided by the natural sympathy of lawmakers, the strategic situation in the Mideast and by a sophisticated pro-Israel lobby whose supporters also work in political campaigns and make substantial campaign contributions.

Israel has rarely enjoyed clear sailing economically in its 37-year history as a Western-oriented, industrializing country beset by enemies in a hotly-contested corner of the Middle East.

But its current economic plight, according to MIT Professor Stanley Fischer, an adviser to Shultz on the Israeli economy, was reached "largely as a result of bad economic policies followed from the end of 1980 to 1984."

Israel was governed during that period by the Likud governments of Menachem Begin and Yitzhak Shamir. They increased government spending, returned Sinai to Egypt, went to war in Lebanon and at the same time increased domestic consumption and imports substantially. The result was soaring budgetary deficits that sharply increased inflation. The increased domestic consumption helped push foreign debt to record levels. Shamir's government fell in March 1984 amid widespread perception of a real economic crisis.

The formation of the Unity government of Labor's Peres and Likud's Shamir last September was justified in large part on the requirement for strong economic measures, which could not be taken by a government whose day-to-day existence was in doubt. When Peres became prime minister, he revealed recently, he was told by economic advisers that "You are going into an almost impossible situation . . . . Inflation will turn into hyperinflation -- 1,000 percent, 2,000 percent -- you will lose control. Unemployment will reach hundreds of thousands of people . . . . The (foreign exchange) reserves will last until April. That is what they told me."

One answer that came quickly to mind was more U.S. economic aid to Israel, which has grown rapidly in recent years. From the first U.S. aid program in 1949 through 1970, total U.S. aid averaged a little more than $60 million per year -- about $1.5 billion altogether for the two decades. The sums jumped massively after the 1973 war, as the United States came to Israel's defense and later as U.S. administrations compensated Israel for diplomatic and territorial compromises. Between 1974 and 1981, total U.S. aid amounted to $18 billion, two-thirds of it for military assistance. Reagan has continued and increased the aid levels.

More importantly, however, the Reagan era has seen a little-noticed but significant change from loans, which have been a large share of aid to Israel and most other countries, to outright grants from the U.S. Treasury. Since fiscal year 1985, none of the aid to Israel need be repaid.

When Peres came last October, he was met on arrival by Shultz, who quickly launched a discussion of the economy in a meeting that had been scheduled to last an hour but that continued for nearly 21/2 hours. According to participants, Shultz made clear from the first that the quid pro quo for new U.S. aid was a turnaround in Israeli economic policies, in Israel's own interest.

It is not clear even today who proposed conditioning the increased aid on Israeli actions. Yuval Elizur, a prominent Israeli economic journalist, said the idea actually originated with Israelis who felt that only U.S. pressure could bring about needed internal reform. For years some high level Israeli officials have been complaining of the unchecked economic excesses in Jerusalem.

Many saw the crisis as an opportunity for the Israeli government to use American pressure as an excuse for taking hard but necessary measures that would be politically unpopular. An aide to Peres said, "He (Peres) did not invite American pressure. But in retrospect it was useful."

Right from the start, according to a variety of Israeli and American sources, Peres and the Americans differed over the severity of the approach to be pursued. This difference has continued down to the present.

In a speech last month in Tel Aviv, Peres said the U.S. officials had suggested two ideas for economic recovery: "One in effect a large devaluation, and the other to abolish linkage." Devaluation would lower the value of the Israeli shekel in relation to other currencies, making imports to Israel more expensive and exports more attractive. Linkage is the Israeli system of indexing local wages and interest rates to the cost-of-living, a system that perpetuates inflation.

Peres said he responded to these proposals by telling the Americans, "While that might bring economic recovery, we won't accept it . . . for our own reasons." An aide to Peres said, "The Americans finally came to accept that he (Peres) is the best judge of what Israel can do. And he said we can't have 400,000 to 500,000 unemployed workers in the streets." (Last week Peres boasted that despite economic woes and some remedial measures there is almost no unemployment in the country.) He also told Shultz, the Israeli official said, that "the roots of the linkage system are historical and the only way to do away with them is in a gradual manner."

U.S. officials, leery of seeming to dictate terms to their sensitive ally, have declined to say publicly what specific measures they recommended for Israel after the early meetings with Peres. But a mid-December letter from Shultz to Peres, which leaked to an Israeli newspaper, was reported to have set forth such austerity measures as large- scale cuts in government spending levels and in support for costly projects, a major cut in subsidies and an end to the Bank of Israel's subservient role in printing money to cover the government's budgetary deficit.

By mid-January it was clear that the bold, comprehensive approach urged by Washington had been rejected in Jerusalem. The Peres government, against the advice of Israeli economists who wanted to do much more, adopted a gradualistic, hold-the-line program in a new wage-price "package deal" with labor and management.

Adoption of the gradual program was "a fact of life" that the U.S. administration had to accept, said a State Department official. Another fact of life was that Shultz and the administration were under increasing congressional attack for their hesitation about emergency U.S. aid to Israel. Some of the lawmakers made it plain they did not want to wait for an Israeli reform program.

"By early this year the American approach had changed," said an Israeli official. "Instead of telling us, 'This is what is required,' they began to ask us, 'What do you think is required?' and 'How are you going to measure your progress?'" In a Washington meeting, Shultz and Israeli Finance Minister Yitzhak Modai sought to create "common ground," as a U.S. official called it, by saying that Israel would prescribe its own economic medicine and draw up "bench marks" to establish how well the cure is working.

To assist the planning process, Shultz dispatched Herbert Stein, chairman of the Council of Economic Advisers under President Nixon, along with MIT's Fischer, to Jerusalem to discuss a program of gradually- imposed remedial measures. After lengthy meetings, Stein in late March drafted a 10- point plan with help from Emmanuel Sharon, chief civil servant of the finance ministry in Jerusalem.

This sketchy document, which is titled simply "Herb's 10 Points" to minimize its official status, was described by Stein in a recent interview as "really subject headings for a program" rather than a program itself. "Herb's 10 Points" were extremely general and, unlike an International Monetary Fund austerity program, did not contain any specific numerical limitations. For example, "Herb's" first point that "The (Israeli) government will adopt an inflation target as a commitment for fiscal year 1985- 6" without saying what that guideline should be.

"Herb" specified that Israel would pass a "budget law" for the first time making ministers accountable if their ministries exceed their budget allocations. The measure has passed the Knesset (parliament) but its implementation is still in doubt.

The large-scale devaluation of the shekel originally proposed by Washington was nowhere to be found in "Herb's" points. Instead the document said simply, "The real effective interest rate will not be appreciated." In fact, the shekel has been losing value against the dollar almost continuously. From an official rate of 10 shekels to the dollar in 1981, the value of the Israeli currency had dropped to 932 per dollar at official bank windows in early May and close to 1,200 per dollar from money changers in Jerusalem.

"Herb's Points," described by Peres as a "10-point framework," were officially presented to the Israeli cabinet April 14. Eight days later Peres sent a confidential letter to Shultz promising some sort of action in each area. Once again, no numerical targets were mentioned. For example, Peres promised that "the government will set quarterly inflation targets." He did not say what those targets would be, and in fact they have not yet been established.

On April 21, the day before Peres' letter arrived, Shultz, in a speech to the American Israel Public Affairs Committee (AIPAC), the leading pro-Israeli lobbying organization, said that "Israel must pull itself out of its present economic trauma . . . . No one can do it for them . . .our help will be of little avail if Israel does not take the necessary steps to cut government spending, improve productivity, open up its economy and strengthen the mechanisms of economic policy. Israel and its government must make the hard decisions."

At the same time, Shultz was feeling the heat from members of Congress, 100 of whom -- 33 senators and 67 House members -- attended a dinner of the AIPAC convention where he had spoken. Reflecting the pressures, Shultz's own bureau of Near East and South Asian affairs had recommended five times, to no avail, that he approve the aid lest he become irrelevant to the process.

On April 29, Shultz finally told his staff he had decided to hold out no more against the emergency aid. Both Israelis and Americans say he made it clear all along that he eventually would approve the aid, but that he was determined to create maximum pressure in Israel for economic reforms. Shultz acted on the basis of Peres' answers of April 22, which were described by Stein as "not as qualitative as they might be, but they represent movement, a process." Fischer said they are not yet a coherent program, but "a set of measures that are helpful but won't solve the problem."

Following Shultz's advice, Reagan on May 15 officially asked Congress to approve the $1.5 billion in special aid to Israel. He had little choice but to act. The House Foreign Affairs Committee and the House appropriations subcommittee had already approved the funds. The Senate acted that same day.

In Jerusalem on that day, the Israel Central Bureau of Statistics jolted those who thought the worst was over when it reported that the April inflation rate was 19.4 percent, which projects to an annual rate of 320 percent. The Israeli economics minister, Gad Yaacobi, called the increase "cause for sharp alarm." The new figures only added to growing skepticism that the current government's policies are strong enough to deal with its problems.

Through a series of political, strategic and diplomatic developments, the United States and Israel have forged a vital alliance that verges increasingly on a partnership. The developments since last October have extended their intimacy in the economic field to an unprecedented degree. Much is riding on what happens now in Israel's economy, an area where the opportunity for reform may be slipping away.