As Air Force One took off from Israel’s Ben Gurion Airport last week, taking President Bush off to the second leg of his Middle East tour, the air of optimism surrounding peace prospects in the region gave way to a more sober and downbeat approach. The promise held out by Bush of an Israeli-Palestinian peace accord before year’s end is now regarded, by experts and policymakers in Jerusalem and Washington, as unrealistic or even misguided.

The main obstacle to an accord, which was not resolved during the president’s visit, remains the political weakness of the respective Israeli and Palestinian leaders, Ehud Olmert and Mahmoud Abbas. While Bush’s attempts to strengthen the two drew praise from analysts, all agree that it will have little effect in the long run. Olmert’s dire political situation became obvious in the days following Bush’s visit, as a major coalition partner left his government due to the talk of such final-status issues as Jerusalem.

“Olmert cannot do anything beyond political survival,” said Yaron Deckel, chief political commentator on Israel’s Channel 1 Television. “He can probably survive this crisis, but the question is, what can he do after that? The answer is — nothing.”

Bush made every effort during his three-day stay in Israel to bolster Olmert’s leadership. He publicly declared support for Olmert and even asked Cabinet ministers, during a dinner hosted by the prime minister, to cut their leader some slack and not break up his coalition. Meyrav Wurmser, director of the Hudson Institute’s Center for Middle East Policy, said Bush was successful in strengthening Olmert during his visit.

“Olmert was embraced by the U.S. administration, and for Israel’s public opinion, this embrace is extremely important,” she said.

“The Israeli public is tired and indifferent to the peace process,” Wurmser said, and because Olmert’s possible replacements — Benjamin Netanyahu of Likud and Ehud Barak of Labor — enjoy little support, Olmert can use the American embrace as a political lifeline.

Within his fragile coalition, however, Olmert’s political future faces threats from all sides. On the right, the Yisrael Beiteinu party of Avigdor Lieberman declared on Wednesday that it will leave the government because of Olmert’s willingness to discuss the “core issues” of the conflict with the Palestinians. On the left, Barak is facing pressure within his party to quit the government once the final report of the Winograd Commission is published January 30. The commission, which is scrutinizing government actions taken during the 2006 war in Lebanon, is expected to issue a damning assessment of Olmert’s wartime leadership and decision-making.

The political problems facing Palestinian leader Abbas seem to mirror Olmert’s. Having failed to garner popular support for his pro-negotiation agenda, Abbas was looking to Bush’s visit for a boost. Bush’s choice of language, in public speeches in Jerusalem and Ramallah, showed a genuine effort to help Abbas.

“There should be an end to the occupation that began in 1967,” Bush said on January 10, winding up the Israeli-Palestinian portion of his tour. He also stressed the need to freeze Israeli settlement activity and remove unauthorized outposts. “The establishment of the state of Palestine is long overdue,” Bush concluded.

“There was nothing new about the language Bush used, but it was framed differently,” said former Middle East envoy Dennis Ross. Still, he argued, Bush’s words will not be enough to rebuild Abbas’s political base.

“America’s increased involvement only has a temporary effect,” Ross said. “The problem is that if nothing changes on the ground, this effect dissipates very fast.”

One of the options discussed during the visit, according to reports, was a grand prisoner swap deal leading to the release of Israeli soldier Gilad Shalit in return for Palestinian prisoners, among them, prominent Fatah leader Marwan Barghouti. According to Wurmser, the release of Barghouti — known for his strong ties with Hamas leaders — could help Abbas reclaim Gaza and could also provide Israel with an excuse not to launch a ground operation there. “This could be a deal that would make everyone very happy,” Wurmser said.

So far, Bush’s emphasis on freezing settlement activity and removing unauthorized outposts in the West Bank has not been ignored by the Israeli government. Olmert, speaking by telephone Tuesday to leaders of American Jewish organizations, said of the outposts, “They are unauthorized, they are illegal and they have to be removed.” Olmert has voiced a similarly tough tone in public in Israel.

As for the demand to freeze settlements, the Israeli stance seems more ambiguous. Days before Bush landed in Israel, Olmert announced that any new construction in the West Bank will require his personal approval. Yet, in a private conversation with Republican Senator George Voinovich of Ohio, Olmert said that construction would continue in the three settlement clusters that Israel intends to retain in any final-status agreement.

“These areas are recognized by the U.S. and by the Palestinians as regions which will stay in the hands of Israel, even if Abbas finds it difficult to openly acknowledge that,” Olmert told Voinovich in a January 2 meeting, according to sources briefed on the conversation.

The implementation of the settlement freeze, which is part of the roadmap peace plan, is expected to be one of the main sticking points in the near future. As a sign of increased Washington involvement in micromanaging the conflict, Bush and Secretary of State Condoleezza Rice announced last week the appointment of another American general to oversee implementation of the roadmap. The new monitor, William Fraser, a lieutenant general, will join generals James Jones and Keith Dayton, who are already on the ground trying to rebuild Palestinian forces and promote security cooperation. Past American attempts to ensure that both sides live up to their commitments have proved ineffective, in part because the administration has been reluctant to step in and make judgments on the issue.

“Naming a third general won’t make the difference,” said former envoy Ross, who spent decades trying to negotiate an Israeli-Palestinian agreement under three administrations. “What we need is to push each side to do what they can do, not what they see as impossible.”