Israel has been more strident on the matter because it sees Iran as an existential threat – and because Iran has threatened to wipe it off the map.
It has unhelpfully unearthed a few video memories from the mid-1990s when US-led negotiators appeared confident they had managed to defuse the nuclear ambitions of another international pariah state, North Korea.
That is a reminder that while the diplomats negotiating on behalf of the global powers may sincerely believe they have made the world a safer place, they may also be wrong about Iran, as the Clinton administration was about the North Koreans.
Iran’s enemies remain of the view that the Iranians are hell-bent on acquiring nuclear weapons at some point and have merely agreed to a delay in return for a variety of short-term concessions.
There is a danger now that Saudi Arabia will feel that a nuclear-capable Shia state must be matched by a nuclear capability in the hands of the Sunni states too.
That brings the nightmare of a nuclear arms race in the Middle East a step closer.
And it leaves open the question of how Israel will respond. It already has a nuclear capability of its own, although its policy is never to acknowledge or discuss it.
The Israelis have plenty of allies on Capitol Hill and they may now try to rally Congressional sceptics to undermine White House attempts to sell the deal in Washington.
That strategy does risk worsening the already sour relationship between Mr Obama and Mr Netanyahu, but the Israeli prime minister may calculate that that is a price worth paying.
And ultimately, of course, a deal which Israel considers to consolidate Iran’s status as a threshold nuclear power puts the issue of unilateral Israeli military action back on the table.
Would Israel consider air strikes to degrade Iran’s nuclear infrastructure?
Israel could argue that its persistent threat to launch such an attack helped to create the pressure that led to the Vienna talks. The issue has been on the back burner in recent years as sanctions have been given time to work and the Vienna negotiations gathered momentum.
But one source familiar with Israeli intelligence thinking told us that Israel was still committed to the Begin Doctrine – the idea that a state pledged to the destruction of Israel could not be allowed to acquire the means of destruction.
The Obama administration will find the nuclear deal a tough sell to its allies in the Middle East like Saudi Arabia and Israel – even if it sugars the pill with upgraded weapons shipments.
But as the battle to get the deal past Congress begins, plenty of thought is being given across the Middle East to the difficulties and dangers that lie ahead.