For 20 years, the White House stood guard over the peace process, reserving for itself the role of stewarding Israel and the Palestinians to a resolution of their conflict. Like some Godfather, the US expected unquestioning loyalty.

But Washington’s primacy in the relationship with both the Israeli and Palestinian leaderships is unravelling at astonishing speed.

The crisis has been building for six years. Barack Obama arrived at the White House just as Israel elected one of the most right-wing governments in its history, led by Benjamin Netanyahu.

At their first meeting Obama reportedly told his Israeli counterpart “not one more brick”, insisting on a settlement-building freeze so that Washington could revive the long-stalled Oslo peace process.

Netanyahu soon defied the president, and has been doing so ever since. The latest humiliation – the final straw, according to White House officials – was Netanyahu’s success in engineering an invitation to address the US Congress next month.

By all accounts, the Israeli prime minister hopes to undermine a key plank of Obama’s foreign policy – negotiating a deal with Iran on its nuclear programme – by persuading Congress to stiffen sanctions against Tehran. That risks a crisis that might ultimately drag the US into war with Iran.

But Netanyahu is not alone in testing Obama’s power. The Palestinian president, Mahmoud Abbas, has also recently chosen to bypass the White House. After years of fruitless waiting, he has pinned his hopes on new international sponsors who can help him achieve his goal of statehood.

Ignoring White House injunctions, he has pressed ahead with resolutions at the United Nations and has now deployed his doomsday weapon: joining the International Criminal Court (ICC) at the Hague. Israelis are calling this a “diplomatic intifada” and urging the US to cut its $400 million annual aid to the Palestinian Authority.

Just as with a mafioso boss, Obama is in trouble if he can no longer inspire fear, let alone respect. But the problem is all his own making.

For six years, Netanyahu “spat in our face”, as one White House official memorably observed of the latest crisis, and paid no discernible price for his impudence. Conversely, Abbas has done everything the Obama administration asked of him, and has precisely nothing to show for his efforts.

Both the Israeli and Palestinian leaderships believe separately that they have core – even existential – interests that the White House is now an obstacle to realising.

Abbas’ disobedience is born of necessity. Aware that the US will never act as honest broker in the peace process, he has been forced to turn to international forums, where Washington’s power is weaker, in the hope of forcing Israel to concede a small Palestinian state.

Netanyahu’s move, meanwhile, is based on the risky calculation that he can manoeuvre the US into a confrontation with Iran to maintain Israel’s regional domination. In doing so, he has made two dubious assumptions.

The first is that he can wait out Obama, who has little more than a year and a half left in office. Netanyahu is betting on a hardline Republican successor who will follow his lead against Tehran.

He may well be disappointed. Even assuming a Republican wins, their hawkish campaign rhetoric on Iran will be fiercely tested by the limitations of office. The US intelligence agencies and military will be instructing the next president in the same cold political realities faced by Obama.

And second, Netanyahu believes he can use the Congress to stymie any threat of an agreement between Washington and Tehran. His working assumption is that the Congress is “Israeli-occupied territory”, as a US observer once called it.

Certainly, Israel has enormous sway in the Congress, but Netanyahu is already getting a lesson in the limits of his influence when up against a cornered US president.

Leading Democrats, it seems, are choosing to side with Obama. Nancy Pelosi, the House minority leader, has already warned that many Democrats may boycott Netanyahu’s speech. Others may attend but sit on their hands rather than join in the rapturous applause he received last time he addressed Congress.

And here is one of the several warning signs Netanyahu has adamantly refused to heed.

His – and Israel’s – influence in the US depends on its bipartisan nature. By taking on the president, Netanyahu risks smashing apart Washington’s political consensus on Israel and exposing the American public for the first time to a debate about whether Israeli interests coincide with US ones.

The very rift he is fostering with Obama is likely to rebound on him strategically too. He is giving Tehran every incentive to sign an accord with the western powers, if only to deepen the fracturing relationship between Israel and Washington.

Meanwhile, the ICC has preferred to initiate an investigation itself against Israel for war crimes, even before the Palestinians’ accession, rather than wait for the threats of retaliation from Israel and the White House to escalate.

What the unravelling of the triangular relationship has achieved – stoked by Netanyahu’s intransigence towards the Palestinians and insolence towards the US – is an opening up of diplomatic wriggle room.

Others states, from Europe to Russia, China and Iran, and international bodies such as the ICC, will fill the void left by Washington’s diminishing credibility and start to shape perceptions about the Israel-Palestine conflict.

That could yet have unpredictable – and dangerous – consequences for Israel.