Hassan Rouhani has come and gone from New York. So has Bibi Netanyahu. Barack Obama, the first American president to converse (over the phone) with his Iranian counterpart since the Shah was overthrown, is coping with a government that has shut down for an indefinite period. Where do things go from here?

The initial meeting between Secretary of State John Kerry and Iran’s new American-trained foreign minister, Javad Zarif, went well enough to ensure that the embryonic U.S.-Iranian dialogue would continue in the context of the P5+1 talks with Iran scheduled for October 15-16. So too did the October 2 letter endorsing Rouhani’s overtures signed by 230 out of 290 members of the Iranian Majlis, virtually all of whom are followers of Ayatollah Khamenei, thereby signaling the Supreme Leader’s support for Rouhani’s charm offensive.

On the other hand, Netanyahu’s speech to the UN made it clear not only that he personally, and his government generally, remains skeptical of the man he deems a “wolf in sheep’s clothing,” and that Israel would never tolerate a nuclear Iran, even if it meant launching an attack without the support of any other state (read: the United States).

The Jewish State has never really got past its suspicions of President Obama’s intentions, despite his constant reassurances and beefed up program of military assistance. Jerusalem is well aware of the President’s reluctance to commit American forces to any additional Middle Eastern adventures, most recently reflected in his eagerness to grab the lifeline that Vladimir Putin threw him on the issue of Syrian chemical weapons. The White House’s outreach to Rouhani has only added depth to those suspicions. So too does the somewhat ironic fact that Khamenei, Israel’s implacable opponent, thus far appears to have endorsed Rouhani’s overtures. If Khamenei supports Rouhani, goes the Israeli logic, then there is no substance to any Iranian willingness to dismantle its nuclear program. The two men are simply buying time, as the Islamic Republic has done in the past when its nuclear-weapons program encountered technical hurdles that it had to overcome.

Israeli concerns notwithstanding, there is little to lose and much to gain in exploring a possible thaw with Iran, as long as Washington, and, for that matter, Europe, does not ease the sanctions that clearly are strangling the Iranian economy. It is clear that any deal would have to include reassurance that the West will not attempt to unseat the Ayatollahs, and permit Iran to “save face” on the nuclear issue by enabling it to maintain a truly peaceful program. Nevertheless, maintaining such a program is not necessarily synonymous with possessing an enrichment capability, and there is some evidence that the Western powers are prepared to make some concessions to Iran on this issue. Were the West to do so, it may be difficult for Obama to deliver on any promises to ease the American economic sanctions on Iran.

In order to have sanctions lifted, Obama will need to persuade Congress to pass legislation to that effect. Yet as the government shutdown has demonstrated once more, the President’s relations with Capitol Hill are in reality virtually non-existent. Indeed, if as Mr. Obama himself put it, “one faction of one party” could force its party, its chamber, and the Congress, to torpedo any agreement with the White House that would keep the government open (leaving aside the fact that neither the White House nor Congressional Democrats were prepared to reach any agreement that did not involve total capitulation by the other side), how much less likely would he be to get a Congress that overwhelmingly supports Israel on a bipartisan basis if Bibi Netanyahu stresses that easing sanctions will endanger his country’s survival. In other words, to have any sanctions lifted, the President will need Mr. Netanyahu's blessing. As for the Europeans, should they seek to go their own way and lift sanctions in support of a deal that the Congress would reject, Capitol Hill could simply respond by imposing even stricter penalties against any European entity doing business with Iran.

It should be noted that even were Israel to acquiesce to an American deal with Iran, the Congress may be reluctant to lift those sanctions that address Tehran’s abysmal human-rights record, or those imposed because of its support for international terrorism, which has cost many American lives over the past three decades. From Iran’s perspective, the reasons that led the Congress to adopt sanctions would matter very little. The Ayatollahs would stress that they must all be removed. Moreover, Khamenei in particular may not be satisfied with an American offer for a partial lifting of sanctions; nor might he trust American guarantees to avoid regime change after seeing the White House jettison its long time ally Hosni Mubarak and turn on Muammar el-Qaddafi within a few short years of obtaining his agreement to drop his support for terrorism. In addition, much in the same way as the Congress is likely to pay heed to Bibi Netanyahu’s concerns, Khamenei will have to do the same for the Revolutionary Guard, whose hatred for all things Western, and especially all things American, is as visceral as it was during the early years after the 1979 revolution.

It is clear, therefore, that the likelihood of a successful deal to terminate Iran’s nuclear-weapons program rests heavily on the preferences of two men, the Prime Minister of Israel and the Supreme Leader of Iran. Both of them have the ability to wreck the negotiations, either directly in the case of Khamenei or indirectly in the case of Netanyahu. Barack Obama will have to work very hard to convince both men to accept a deal that he desperately wishes to consummate (and thereby at last justify the Nobel Prize he received so prematurely in 2009). Whether he has the ability to do so is an open question. First he must demonstrate that he can work with his fellow Americans to reopen the government. If he cannot successfully negotiate with Capitol Hill, he is unlikely to do better with two wily and hardheaded antagonists with whom his relations have been poor in one case and nonexistent in the other.

Dov Zakheim served as the undersecretary of defense (comptroller) and chief financial officer for the U.S. Department of Defense from 2001–2004 and as the deputy undersecretary of defense (planning and resources) from 1985-1987. He also served as DoD's civilian coordinator for Afghan reconstruction from 2002–2004. He is a member of The National Interest's advisory council.