JERUSALEM — Israeli and Palestinian leaders left New York and the annual meeting of the UN General Assembly in ongoing disagreement over the substantive issues America wants to see them negotiate to achieve peace. But if the neighboring cities could not be further apart on the core issues that divide them, they seem strangely unified by a new and deepening mistrust toward Washington.

If U.S. President Barack Obama hopes to influence both parties toward a peace deal in a possible second term, Palestinian and Israeli misgivings are so widespread that they could leave his administration with its hands tied. Rudderless, American leadership could prove a precarious factor as the Middle East still reels from unprecedented societal unrest and the overthrow of previously secure dictators.

Meanwhile, others hope to step into the breach. French president Nicolas Sarkozy and Spanish Foreign Minister Trinidad Jimenez used their UN platform in essence to offer themselves as alternative potential peace brokers.

The morning after: In Jerusalem, pessimism reigns after UN speeches

Arab countries that have presented themselves as possible sponsors for Israeli-Palestinian negotiations in the past, such as Saudi Arabia or Jordan, are too preoccupied with their own internal crises to attempt an intervention now. Hoping to stave off the kind of protests that have toppled other regional strongmen during the Arab Spring, Saudi Arabia’s King Abdullah granted women the right to vote yesterday, but has had almost no comment about Palestine’s predicament.

Palestinian President Mahmoud Abbas, embraced by jubilant crowds upon his return to Ramallah, made a point of stressing that his regime faces no such internal discord.

In Ramallah, however, there is a universal and bitter disillusionment about the first American president they hoped might tilt toward their cause. Obama’s 2009 speeches in Cairo and in Istanbul, in which he addressed the Muslim world directly, created something akin to irrational exuberance about the possibility that the new American leadership would efface past tensions and champion the cause of Arab nations.

In Jerusalem, early concerns about an untested president with a Muslim middle name and a much cooler demeanor than that of his predecessor toward Biblical geography has ripened into the conviction that Obama is simply not on Israel’s side. Obama’s failure to visit Israel while president and the same two speeches, in which the Israeli state barely figured, has created a profound sense of unease among a wide range of Israelis. From the Israeli point of view, it appears Obama took Israelis’ trust in him for granted, and simply forgot to address them during his first term.

Related: How the French differ with Obama over Palestine

As a result, American credibility is at an unprecedented low in both societies and in both governments.

“Obama has disappointed us completely. If you analyze his language from the Cairo speech and then look at what he is saying today — everything he said about justice has simple vanished,” said Xavier Abu Eid, an advisor to the Palestinian negotiating team.

“President Obama spoke very proudly at the UN about international intervention in Libya, Afghanistan, Iraq, and he spoke of the important role of the UN. But when he spoke of the Palestinian state he indicated that UN intervention would not bring peace. So it seems the UN and joint international initiatives can work anywhere in the world but in Palestine.”

It took Palestinian Foreign Minister Riyad al-Malki less than 24 hours to reject a new proposal for the renewal of negotiations made by the Quartet — the United States, Russia, the United Nations and the European Community — following the Palestinian bid for statehood on Friday.

Speaking to Palestinian radio, al-Malki said that the Quartet's proposal does not call for a freeze of Israeli settlements in the West Bank or a withdrawal to the 1967 lines, and is therefore insufficient.

The Quartet, represented by British former prime minister Tony Blair — who has made of Jerusalem a second home in recent months while attempting, and failing, to renew bilateral negotiations between the Israelis and the Palestinians — has requested from both parties comprehensive proposals within three months on territory and security, and substantial progress within six months. Sarkozy proposed a year-long schedule of negotiations culminating in the declaration of Palestinian statehood.

More: Is this the end of Israel as we know it?

Israel’s far-right foreign minister, Avigdor Lieberman, as implacable a foe of negotiations with the Palestinians as he is of Obama, and who looks set to present a formidable electoral challenge to Prime Minister Benjamin Netanyahu, surprised everyone by accepting the Quartet’s terms and initiative.

“Obama’s speech at the UN was a speech any Israeli would sign off on,” said Adar Primor, the foreign news editor for the daily Israeli newspaper Ha’aretz. “So there’s a minimum of gratitude you have to show. If they don’t thank Obama for this speech, what are they ever going to thank him for? But I don’t think this speech indicates that Obama has changed his convictions in any way.

“I think that Obama faces a tough electoral year and he needs Congress and needs [the Israeli-American public]. I have the feeling that if he could have said what Bill Clinton said last week — that Netanyahu is entirely to blame for the failure of negotiations — that he would have. I don’t know, but I wonder if they coordinated their messages so that Obama would make the speech he was constrained to make but the anti-Netanyahu message was nonetheless heard.”

Israel media reported on Obama’s manifestly pro-Israeli UN speech with giddy fervor, as if a wavering American president had finally seen the light. But Primor is skeptical about its long-term effects.

“In broad strokes, the feeling in Israel is that an overtly Zionist president was replaced in the White House by someone with the opposite tendency. His name made people fearful, and the fact that he went to Egypt and to Turkey but has never seen the need to come here and speak to us …. People are taking the UN speech with a big pinch of salt. They think it is not really Obama, only the electoral year version of him.

Obama has been a disappointment to all, Primor says.

“The minority who hoped he’d move things, that with his personality and newness he’d be able to change things, have seen that they were wrong. And those who always thought he might be difficult for Israel remain disappointed.”