Barack Obama thinks Benjamin Netanyahu’s relentless construction of Jewish homes over the Green Line could spell the death of Israel, and several new appointments to key positions in the prime minister’s government only intensify that concern. Benjamin Netanyahu thinks Barack Obama underestimates the dangers posed by Iran’s nuclear program, and the president’s latest sanguine talk about Tehran being a year-plus away from the bomb only underlines that conviction.

For all that the president’s visit this week is being carefully choreographed as a seamless fiesta of warm handshakes and solidarity stops, therefore, Obama’s 51-hour Israel sojourn will bring together two leaders struggling to hide their respective convictions that they know better how to safeguard not only their own country but also their counterpart’s. There’s no doubt that the alliance between the two countries is solid, deeply rooted, based on a range of genuine common values and interests, and particularly important given the Middle East’s current instability and unpredictability. Unfortunately, there’s also no doubt that each of these two particular leaders believes the other is disastrously wrong-headed. And if that gulf between them is not bridged, it could have phenomenally damaging consequences.

Interviewed by this writer when he visited as a presidential candidate in 2008, then-Senator Obama expressed no empathy for Israeli claims over the pre-1967 lines, declaring flatly that the Israelis have to decide “whether getting that buffer is worth the antagonism” it causes the Palestinians. Two years ago, unveiling a largely forgotten blueprint for diplomatic progress, he described the future of Judea and Samaria as “perhaps less emotional issues.”

Time after time, he and his administration officials, publicly and in private, have indicated that they simply cannot fathom Israeli settlement policy — increasingly appreciating the historic connection to the Land but still finding themselves baffled by the Israeli right’s determination to realize that connection to colossal self-defeating effect: You rightly insist on retaining a Jewish and a democratic Israel, runs their reasoning, so why relentlessly jeopardize that imperative by building more and more homes in areas you will need to relinquish?

The staffing of the new Netanyahu government will have confirmed Washington’s fears: The staunchly pro-settlement Jewish Home, whose leader Naftali Bennett wants to annex 60 percent of the West Bank, is a vital coalition partner, and several of its most prominent settlement activists have been placed in key government positions. Bennett himself will have considerable influence as a minister with responsibility for economics, trade and Jerusalem affairs. Nissan Slomiansky will head the powerhouse Knesset Finance Committee. And Uri Ariel, who is so desperate to annex the entire West Bank that he last year authored a paper asserting that this could be done without harming Israel’s Jewish and democratic nature, is the new minister of housing.

Ariel announced on Sunday, before even taking up his post, that any new settlement freeze would be a “dreadful” idea and that building in Judea and Samaria would continue as usual. Netanyahu’s No. 2, former and would-be future foreign minister Avigdor Liberman, on Monday also ruled out a settlement freeze. And Ze’ev Elkin, named by Netanyahu as deputy foreign minister — to hold the fort while Liberman fights fraud and breach of trust charges — shares Ariel’s desire to annex the entire West Bank. “For 20 years, we talked about what to give and why. Now the time has come for an entirely different discourse,” Elkin declared at a conference on the issue exactly a year ago. “This is our land, and it’s our right to apply sovereignty over it. Regardless of the world’s opposition, it’s time to do in Judea and Samaria what we did in [East] Jerusalem and the Golan.”

Netanyahu is not entirely deaf to demographic concerns, not entirely unmoved by the worry that untrammeled settlement construction will boomerang. Remember, he did freeze settlement building for 10 months from November 2009 to September 2010, at Obama’s behest, in a failed effort to draw Mahmoud Abbas back to the peace table. But he faults Obama for underestimating Arab hostility to Israel — and lectured him to that effect in the Oval Office in May 2009, telling a stone-faced president why Israel could “not go back to those indefensible [pre-'67] lines” — and for the absence of nuance in US settlement policy.

It is unhelpful to Israel and to the prospects of negotiated progress, his aides argue, that the US administration formally deems building in Gilo or Ramat Shlomo — the East Jerusalem ultra-Orthodox neighborhood where new construction plans sparked a spectacular US-Israel bust-up when Vice President Joe Biden visited in 2010 — to be as problematic as construction in isolated settlements deep in the West Bank.

America’s dismissal of all construction over the Green Line as unacceptable, Netanyahu would claim, has actually had the effect of keeping Abbas away from the peace table. For how can the Palestinian Authority president, who is prepared to countenance Israel’s annexation of some Jewish-settled West Bank areas in return for one-for-one territorial compensation, allow himself to appear more pro-Israel than the Americans by talking to an Israeli government whose behavior is subject to such criticism from the US?

On Iran, too, a Jerusalem-Washington disconnect continues to play out, with potentially devastating repercussions.

Netanyahu plainly feels that he was fated to serve as Israel’s prime minister when the Jewish nation is again subjected to genocidal threat. If his father Benzion lacked the wherewithal to avert or minimize the tragedy of the Holocaust he saw coming 75 years ago, then his son is determined to ensure that history not repeat itself.

The prime minister said last week that the Israeli public has failed to recognize how grave are the threats to its very existence, and again in the Knesset on Monday cited the imperative to thwart Iran as the top priority of his new government. He sees Iran, moreover, as a threat to Israel and the rest of the free world, regarding the regime as ideologically and territorially rapacious, and unpredictable. Obama, he believes, underestimates the ayatollahs, and naively over-relies on a rationality and a pragmatism that they simply may not share.

He failed very publicly last year to persuade Obama to specify a “red line” that, if crossed by Iran, would prompt US-led military intervention, and may only have been deterred from initiating a strike himself by a combination of vocal US opposition and profound reservations from within Israel’s own security establishment.

Netanyahu is not convinced that the US would have time to act if the Islamic Republic is allowed to become a “breakout” state, with enough highly enriched uranium and the necessary delivery systems to make a dash to the bomb in a matter of weeks. Hence his call at the UN last September to stop the Iranians at the enrichment stage, a call Obama at one point appeared to dismiss as irritating “noise.”

For its part, the administration worries that Netanyahu underestimates the consequences of military intervention — for Israel, the US and the rest of the West. Obama remains convinced that Tehran can yet be dissuaded from pursuing the bomb by a combination of diplomatic carrots and economic sticks, and that even if that mix fails, as he noted in an interview last week, the moment of truth is still a fair distance away.

You can trust me, he will essentially assure Netanyahu. If all else fails, I will resort to force. I’m not bluffing. And if I act, I will have much of the international community with me, and I’ll be able to cause the Iranians far more damage than an Israeli strike could achieve.

Trouble is, for all those smiling, side-by-side photo-ops we’re going to witness in the next few days, Netanyahu doesn’t fully trust Obama, and is certainly wary of trusting him with the future of the Jewish nation. And Obama doesn’t fully trust Netanyahu, the irresponsible settlement-builder, not to act irresponsibly too on Iran.

If, against all odds and in defiance of all precedent, the presidential visit can somehow change that dynamic, it will be historic indeed. More likely, though, is that Obama will head home, scratching his head as ever at the frustrating wrong-headedness of the leader of that astonishingly gutsy little Israel. And Netanyahu will wave Obama farewell, lamenting the inexplicable failure of the leader of the free world to effectively utilize the extraordinary influence and raw power at his disposal.