Alone in his study at Camp David's rustic Aspen lodge, Jimmy Carter gazed out the window at Maryland's Catoctin Mountains and bowed his head in prayer. After 10 days, peace talks with Israeli Prime Minister Menachem Begin and Egyptian President Anwar Sadat had broken down, apparently for good. Aides began drafting a speech for Carter announcing that the Camp David summit had failed.

The speech was never delivered, of course. The 1978 talks ended in a triumph for American diplomacy, setting the stage for Egypt's landmark peace treaty with Israel and laying the foundation for U.S. efforts to broker a settlement between Israel and the Palestinians, whose 52-year struggle over land and identity is the core of the Arab-Israeli conflict.

Now history has come full circle. On Tuesday, President Clinton will attempt to complete the process that Carter began at Camp David, returning to the presidential retreat with Israeli Prime Minister Ehud Barak and Palestinian leader Yasser Arafat with the goal of forging a so-called permanent status settlement by the two parties' agreed-upon deadline of Sept. 13.

As if the task were not already difficult enough, Barak's governing coalition appeared headed for collapse yesterday as three parties announced that they were deserting him out of fear that he would give too much away to the Palestinians. Opposition parties, meanwhile, scheduled no-confidence votes today in the Israeli Knesset. Even if Barak survives the no-confidence votes, the crumbling of his coalition on the eve of the Camp David summit could undercut his ability to negotiate with the Palestinians by leaving him in charge of a minority government.

Following Carter's example, Clinton is making a leap of faith--gambling that the right combination of carrots and sticks will nudge the two leaders toward closing wide gaps over basic issues such as borders, refugees and the status of Jerusalem. With just six months left in office, the president has concluded that the gradual approach to peacemaking that began with the 1993 Oslo accords--with its prescription for incremental land transfers, economic cooperation and other trust-building measures--has outlived its usefulness and that the time has come for hard choices.

"We have been locked in a chain of hostilities for the last 52 years with the Palestinians," said one of two well-placed Israeli officials who briefed reporters on the talks Thursday. "We feel that a moment of truth is here."

The stakes could hardly be higher. With Arafat having vowed to declare a state by Sept. 13 even in the absence of an agreement, U.S. and Israeli officials--and, for that matter, the Palestinians themselves--fear that a failure at Camp David could trigger armed clashes between Israeli troops and Palestinian security forces. That prospect has prompted talk in foreign policy circles that Clinton may ultimately pursue a partial settlement--in effect, another set of Oslo accords--that defers action on the critical question of Jerusalem but avoids crisis by keeping the diplomatic wheels turning.

For now, however, neither party is willing to discuss such an outcome in public, insisting that they are traveling to Maryland with open minds and a genuine desire to settle their conflict once and for all. In Thursday's briefing, for example, one of the Israeli officials said Barak might agree to hand over the Jordan Valley--long regarded as an essential buffer against attacks on Israel from the east--to the Palestinians in phases in return for adequate security guarantees.

In the same vein, the official suggested that Barak was prepared to redraw the boundaries of Jerusalem to incorporate Palestinian areas--thus providing Arafat with the potential to fulfill his long-held dream of a capital in the holy city--in exchange for the absorption into Israel of nearby Jewish settlements in the West Bank.

"Everything about Jerusalem is on that table at this summit," the official said, adding that Barak is "prepared to go the extra mile on this topic."

At least when addressing Palestinians, Arafat has continued to sound a hard line, insisting that Israel hand over all of Gaza and the West Bank, which it captured from Jordan in the 1967 Middle East War, and grant Palestinian refugees the "right of return" to homes they lost when Israel was founded in 1948. But the Palestinian leader has shown more flexibility in private, according to a senior State Department official who speaks with him often; some analysts do not discount the possibility of a breakthrough.

"Unofficially, there's been a loosening of positions, and there are contours that are emerging on the major issues," said Shibley Telhami, a senior fellow at the Brookings Institution who also holds the Anwar Sadat Chair for Peace and Development at the University of Maryland. "It's a gamble, but it's an inevitable gamble. . . . There is a reasonable chance that it could work."

The story of the first Camp David summit is instructive. Ever since Egypt's unsuccessful attempt to recover the Sinai Peninsula from Israel in the 1973 October War, U.S. mediators had pursued a "step-by-step" approach to Middle East diplomacy, seeking to ease tensions through modest confidence-building measures. Then came Sadat's historic 1977 decision to break with his fellow Arab leaders and travel to Jerusalem, where he addressed the Israeli Knesset.

But Sadat's bold initiative was followed by stalemate, raising fears in Washington of another slide toward war. In Carter's view, "this was the first time an Arab leader had been willing to take that kind of a risk, and if it came to naught, Lord knows how long it would be before Sadat or any other Arab leader would be willing to try it again," recalled Jody Powell, Carter's press secretary at the time.

So Carter invited the two leaders to Camp David, hoping that secluded talks in an intimate setting--coupled with the prospect of generous American aid to both parties--could fulfill the promise of Sadat's trip to Jerusalem. As Carter wrote in his memoir, "Keeping Faith," "I was convinced that if we three leaders could not resolve the very difficult issues, some of which had never been addressed forthrightly, then no group of foreign ministers or diplomats could succeed."

U.S. officials made elaborate preparations, supplying Carter with thick briefing books on each leader and arranging for Egyptian and kosher chefs to cook for the two visiting delegations. Each leader stayed in his own cabin, with Carter often strolling between them to present new proposals. One day he took Begin and Sadat on a tour of the nearby Gettysburg battlefield.

It was a diplomatic high-wire act that came perilously close to disaster. According to Carter's account, Begin's insistence on maintaining Jewish settlements in the Sinai infuriated Sadat, who at one point packed his bags and arranged for a helicopter to pick him up. Carter, too, grew exasperated with the hard-line Israeli. "You are as evasive with me as with the Arabs," he told Begin in one heated exchange. "The time has come to throw away reticence. Tell us what you really need."

According to Zbigniew Brzezinski, Carter's national security adviser, it was only after Carter threatened to publicly blame Israel for the collapse of the talks that Begin finally relented on the settlement issue. Begin's concession helped save the summit. In March 1979, Sadat and Begin returned to Washington to sign the peace treaty that restored the Sinai to Egypt and paved the way for the first exchange of ambassadors between Israel and an Arab state.

In theory, at least, the Camp David accords also laid the groundwork for establishing Palestinian self-rule. But Begin proved far more resistant on that front than he did to returning the Sinai to Egypt. Indeed, Sadat's decision to make peace with Israel with the Palestinians still living under Israeli occupation made him a pariah among fellow Arab leaders and set the stage for his murder by Islamic fundamentalists in 1981.

Clinton will now try to complete the task that Carter began. Under terms of the Oslo accords, Palestinian and Israeli negotiators began discussing a final peace settlement in 1996, although their efforts on that front did not begin in earnest until last September. But in recent months the talks have "reached a plateau," said one of the Israeli officials who briefed reporters Thursday.

No one expects Clinton's job to be easy, not only because of the complexity of the issues but also because he is laboring under a tight deadline. "Carter had two years to go," Brzezinski noted. "Clinton has five months. . . . That puts pressure on him."

"Everybody knew that if the conference broke down, we were quite prepared to blame someone and take the political heat," Brzezinski added. "I'm not sure with elections so near the same degree of credibility attaches to Clinton."

On the other hand, the consensus among foreign policy experts and administration officials is that Clinton probably had little choice but to convene a summit now--perhaps to be followed by another such meeting next month--given the looming September deadline and Barak's growing political troubles at home. "I think it's a risk worth taking, because right now we are on a drift toward crisis," said Richard N. Haass, director of foreign policy studies at the Brookings Institution and the former top Middle East specialist in the Bush White House.

Besides the threat of blaming one side or another if the talks fail, Clinton also has substantial carrots to offer. Israel, for example, is eager for high-tech American weaponry; the Palestinians will expect a generous international aid package--paid for by the United States, Europe, Japan and Saudi Arabia, among others--and last week floated a figure of $40 billion as compensation for refugees.

Eager to avoid blame if the talks fail, Israeli officials have sought to project an image of moderation and flexibility, a theme that came through strongly in the briefing for reporters Thursday.

One of the briefers, for example, made clear that Barak has no intention of signing an agreement that restores Israel's 1967 borders, as Arafat has insisted. On the other hand, the official said that Barak is prepared to turn over outlying Jewish settlements in the West Bank, with the proviso that the Palestinians "acknowledge the right of Jews to live in those areas" under Palestinian rule if they choose.

Few settlers, of course, would likely remain in the West Bank under those conditions. By making their departure voluntary, however, Barak would avoid the politically embarrassing spectacle of Israeli troops forcibly removing settlers from their homes.

Barak will not accept a right of return for Palestinian refugees, the official said. But he is prepared "to show empathy" for the refugees' plight and to "talk about family reunification" in cases where refugees can show they have relatives living inside Israel, the official said.

Jerusalem is widely regarded as the toughest issue. But here, too, Israeli officials are hinting at creative solutions linked to the incorporation of nearby West Bank settlements into Jewish areas of the city. "This implies opening up the borders of Jerusalem and that implies lots of interesting possibilities--full stop," one of the officials said.