This is even trickier than it sounds. There’s a lot of chatter right now about Netanyahu forming an Obama-friendly coalition that includes parties to his left, specifically Tzipi Livni’s Hatnuah and Shaul Mofaz’s Kadima, and squeezes out Naftali Bennett of the pro-settler, anti-Palestinian-statehood Jewish Home party. Less noticed is the fact that much of Netanyahu’s own Likud-Beiteinu bloc is vehemently opposed to any form of Palestinian statehood, including at least three of the top 10 members of his Knesset list. Selling his caucus on a diplomatic plank will be the hardest part of his coalition negotiations.

As tricky as Netanyahu’s situation has become, Yair Lapid’s situation may be even trickier. He suddenly finds himself in a global spotlight, the newest star on the world stage as the leader of a revived Israeli peace camp. It’s a position he neither sought nor wanted. Although his own views are relatively moderate and he recruited some strong peace advocates to his list, his campaign was based almost entirely on domestic issues, starting with ending the ultra-Orthodox military draft exemption. His voter base expects him to follow through and demand a government that excludes the ultra-Orthodox parties. They expect speedy action to integrate that cloistered community into the army and the workforce. His natural ally on the issue is Bennett.

Before the election, when he hoped to become the third or fourth largest faction in the Knesset, Lapid had his sights on domestic cabinet ministries such as education and social welfare, which would give him control of his signature middle-class socio-economic causes. Since the election, he and Bennett have conducted a very public flirtation, aiming to corral Netanyahu into adopting their domestic agenda and putting the Palestinians on the back burner. Some of Lapid’s allies are known to believe he should become foreign minister, one of the three top government posts (the third is Defense), as befits his senior political standing, but he’s shown little enthusiasm.

Netanyahu would have been happy to backpedal on the peace process, but he wasn’t enthusiastic about enlisting Bennett, with whom he has a longstanding personal feud. He apparently hoped to bring in the ultra-Orthodox Shas party, using some watered-down compromise on the military draft.

Obama’s announcement changes all the rules. It’s hard to imagine Netanyahu greeting the president as the head of a governing coalition that includes the settlers as ranking partners. Bennett might conceivably swallow some sort of vague peace process to join the cabinet, but the rest of his party won’t. Netanyahu will have to reach to his left, to Livni and Mofaz. But Netanyahu, needing to remain at the center of his own coalition, will need another partner on his right flank. This boosts the prospects of Shas, which has a right-wing voter base but moderate positions on peace issues. Lapid will have to swallow a painful compromise on ultra-Orthodox conscription.

If Lapid still harbors any personal thoughts of taking on a domestic affairs portfolio, he can forget about it. As the unintended leader of the center-left peace bloc he’ll almost certainly find himself in the Foreign Ministry. If he’s smart, he’ll insist on bringing along his ally, former Shin Bet director Yaakov Perry, as deputy foreign minister and chief guide to the convolutions of the peace process. That will cause a fight with Netanyahu’s Likud-Beiteinu allies, who will want to install one of their own hard-liners as deputy minister in order to slow the peace process. It will be up to Lapid’s allies to push him to stand his ground on this.

As an advocate of religious liberalization and pluralism—a rarity in any wing of Israeli politics—Lapid will want to claim the Education Ministry for his number two, Rabbi Shai Piron, a leader of the liberal Orthodox Tzohar movement. Shas will fight this, fearing efforts at religious reform, and will probably insist on putting education in the safe hands of a committed secularist from Likud or Livni’s party. As compensation, they might have to offer Lapid their traditional strongholds in Housing and/or Welfare, natural platforms for his middle-class agenda.

The biggest mystery is the Defense Ministry. Likud back-benchers, already alarmed at the specter of renewed peace talks, have begun thumping for a hard-liner in that key post. Avigdor Lieberman, Netanyahu’s number two, would be the natural candidate, but he’s excluded from the cabinet while he faces criminal corruption charges. Favored to take his place in line is political newcomer Yair Shamir, number four on the list and son of the late ex-prime minister Yitzhak Shamir. Shamir recently authored an essay in the Times of Israel explaining his firm opposition to Palestinian statehood.

Netanyahu will have a hard time accepting Shamir or any other hard-liner in the defense post while Obama is looking over his shoulder. The best candidate for the job—both politically and professionally—would be Mofaz, who has held the post before. Given the complexities of the coalition negotiations, it would be hard to justify giving such a plum post to the head of a two-man Knesset caucus. But there’s a simple solution: invite Mofaz to rejoin the Likud, which he reluctantly left in 2005 to follow Ariel Sharon into Kadima. Mofaz and his number two, former Shin Bet deputy director Yisrael Hasson, would bring the Likud a strong security cachet that it currently lacks. And Netanyahu could welcome Obama with a team that’s tailor-made for tough but fair negotiations.