WASHINGTON/JERUSALEM - Six months after US President Barack Obama eased a strained relationship with Prime Minister Binyamin Netanyahu during a visit to Israel dubbed "Operation Desert Schmooze," the two leaders now face the biggest test of whether they can work together - and the stakes are higher than ever.A diplomatic charm offensive by new Iranian President Hassan Rouhani has suddenly opened up a gap between the White House and Netanyahu's government. How they respond could have far-reaching implications for their political legacies as well as the future stability of the Middle East.Coming three days after Obama and Rouhani had a historic phone call, which was the highest-level contact between the two countries in three decades, Monday's White House meeting between the US and Israeli leaders is shaping up as perhaps their most consequential encounter. Obama and Netanyahu will try to avoid any repeat of previous clashes as they seek to project unity. But behind closed doors, their differences over Iran may prove hard to bridge.Unnerved by the pace of the US outreach to Iran and deeply skeptical of Rouhani, Netanyahu will push Obama for specific steps and deadlines to prevent Tehran from using talks to "run out the clock" while it advances toward making a nuclear weapon."I will speak the truth. Facts must be stated in the face of the sweet talk and the blitz of smiles," Netanyahu said at the airport in Tel Aviv before departing for Washington on Saturday night.Obama will press Netanyahu for time to test Rouhani's intentions, while trying to reassure Israel he will not ease sanctions prematurely. He is likely, however, to resist Israeli pressure for a precise time limit for diplomacy with Iran to produce a deal, according to a source close to the White House."American and Israeli officials like to say there's no daylight between them on Iran," a former US official said. "But with his words alone, Rouhani has opened a window." Looming large is the question of military action against Iran if diplomacy fails to prevent Tehran from pressing ahead with what Israel and the West suspect is a drive to develop nuclear weapons. Iran denies it is seeking a bomb.Some Israeli officials doubt whether Obama has the stomach for attacking Iran after he pulled back earlier this month from a threat to bomb Syria over its suspected use of chemical weapons."It totally suggests that for the president, all options are not on the table with Iran," said Elliott Abrams, a Middle East adviser under Republican former President George W. Bush, now at the Council on Foreign Relations think tank.Further complicating matters is Obama's reinvigorated push for a peace deal between Israel and the Palestinians in talks that restarted earlier this year. Middle East diplomacy is expected to figure more prominently in Monday's meeting than originally thought, after Obama listed it beside Iran as a top priority in his address to the United Nations on Tuesday.Netanyahu will be in anything but a conciliatory mood. One Israeli official suggested privately that Obama was "talking up the Palestinian issue to keep the Sunni Arab world on his side" as he builds bridges with predominantly Shi'ite Iran.NO OVAL OFFICE BLOWUP EXPECTEDObama and Netanyahu have a track record of difficult encounters, including a blowup in the Oval Office when Netanyahu famously lectured the president on Jewish history. He later made no secret of his fondness for Republican challenger Mitt Romney, who lost to Obama in last year's presidential election.Obama made his first presidential trip to Israel in March to reset his relationship with Netanyahu, using some old-fashioned backslapping to move beyond their confrontational past. American journalist Jeffrey Goldberg, an authority on the Middle East, described it as "Operation Desert Schmooze." Although Obama may not have won the hearts of the Israeli public like former president Bill Clinton did in the 1990s, he appeared to make a big dent in their suspicions about him dating from his 2009 speech to the Muslim world in Cairo."He had a very dysfunctional relationship with Netanyahu and they managed to overcome it," said Aaron David Miller, a former State Department adviser now at the Woodrow Wilson Center in Washington. "The idea that he would now pick a fight with the Israelis is improbable. They will look for common ground."But all indications are that the White House talks will be less than a total meeting of the minds. Friday's phone call between Obama and Rouhani is sure to increase Israeli wariness over the prospects of US-Iranian detente, even though the White House gave Israeli officials the courtesy of letting them know in advance.In a nod to Netanyahu's concerns, Obama insisted on Friday he would not do anything to endanger Israel, and a senior administration official acknowledged that "the Israeli government has every right to be skeptical" of Iran.Obama's ability to calm Israel about his engagement with Iran might be limited by the influence of the pro-Israel lobby in Washington and lawmakers on both sides of the aisle who are quick to defend the Jewish state.Robert Menendez, Democratic chairman of the Senate Foreign Relations Committee, and Lindsey Graham, a veteran Republican senator, wrote an opinion piece in The Washington Post on Friday arguing for further oil sanctions against Iran.'CREDIBLE MILITARY THREAT'Netanyahu will be looking for proof of Obama's commitment to confront Tehran with a "credible military threat" if diplomatic efforts fall through. Obama has insisted he is not bluffing, but has not been as explicit as Netanyahu wants.The Obama administration official hinted that the president might go further this time, at least in private, saying the two would focus on "red lines" to prevent Iran from developing a nuclear weapon. Obama has long resisted Netanyahu's demand for a clear and specific ultimatum to Iran on the US use of force, and there is little reason to believe he will issue one now.Netanyahu brandished a cartoon bomb last year in his UN speech to illustrate what he called Iran's progress toward nuclear arms, but Israeli sources predict he will opt for a less flashy message when he addresses the world body on Tuesday.Obama may prefer a more toned-down approach by the sometimes abrasive Israeli premier. But allowing Netanyahu to play "party pooper" - as Israeli media have dubbed it - may serve a purpose for Obama of keeping the heat on Iran while pressuring European partners not to break ranks on sanctions.Some analysts believe Netanyahu's earlier threats helped lead to Iran keeping uranium enrichment below the cartoon bomb's "red-line" threshold - enough medium-enriched uranium for a single bomb - that he suggested would trigger Israeli strikes."The greater the economic and military pressure, the greater the chance of diplomacy succeeding," said Strategic Affairs Minister Yuval Steinitz, a Netanyahu confidant.As Obama moves deeper into his second term, however, he may see rapprochement with Iran after decades of estrangement as part of his foreign policy legacy - especially at a time when he faces criticism for his response to Syria's civil war and Egypt's military takeover.But Obama may be mindful of the damage to his record if, as Israeli leaders suggest, it turns out Iran is just buying time.