As congressional Republicans seek to undermine the nuclear agreement between Iran and the international powers, they assert that hardline Islamists in the Islamic Republic are delighted with the deal, while Israelis concerned over their country’s security are appalled. The same theme is now repeated constantly on Fox News Channel and throughout right-wing media.

But that message is largely false – and in very important respects, the opposite is true.

In arguing for the agreement at American University last Wednesday, President Obama noted that the most hostile factions in the Tehran regime aren’t celebrating this agreement – as the cover of the New York Post suggested. “In fact, it’s those hardliners who are most comfortable with the status quo,” he said. “It’s those hardliners chanting ‘Death to America’ who have been most opposed to the deal. They’re making common cause with the Republican caucus.”

Indeed, while vast throngs of Iranians greeted their government’s negotiators in a joyous welcome, the fanatical reactionaries in the Revolutionary Guard and the paramilitary Basij movement – which have violently repressed democratic currents in Iran – could barely control their outrage. Upon reading the terms, a Basij spokesman said last month, “We quickly realized that what we feared…had become a reality. If Iran agrees with this, our nuclear industry will be handcuffed for many years to come.”

Hoping and perhaps praying for a veto by Ayatollah Ali Khamenei, their Supreme Leader, the Basijis, the right-wing media in Teheran, and their regime sponsors pointed to “red lines” that the agreement allegedly crossed. “We will never accept it,” said Mohammed Ali Jafari, a high-ranking Revolutionary Guard commander.

Such shrill expressions of frustration should encourage everyone who understands the agreement’s real value. Iran’s “Death to America, Death to Israel” cohort hates this deal – not only because of its highly restrictive provisions, but because over the long term, it strengthens their democratic opponents and threatens their corrupt control of Iranian society.

In Israel, meanwhile, the alarmist criticism of Prime Minister Benjamin Netanyahu – a sage whose confident predictions about Iran, Iraq, and almost everything else are reliably, totally wrong – has obscured support from actual military and intelligence leaders. Like experts in this country and around the world, the best-informed Israelis understand the deal’s imperfections very well — and support it nevertheless.

“There are no ideal agreements,” declared Ami Ayalon, a military veteran who headed the Israeli Navy and later oversaw the Jewish state’s security service, the Shin Bet. But as Ayalon explained to J.J. Goldberg of the Forward, this agreement is “the best possible alternative from Israel’s point of view, given the other available alternatives” — including the most likely alternative which is, as Obama explained, another extremely dangerous Mideast war.

Efraim Halevy, who formerly ran the Mossad, Israel’s foreign intelligence service, and later headed its National Security Council, concurs with Ayalon (and Obama). Writing in Yedioth Aharonoth, the national daily published in Tel Aviv, Halevy points out a profound contradiction in Netanyahu’s blustering complaints. Having warned that an Iranian nuclear weapon would pose a unique existential threat to Israel, how can Bibi logically reject the agreement that forestalls any bomb development for at least 15 years and increases the “breakout time” from one month to a year — even if Iran ultimately violates its commitments?

Such a deal is far preferable to no deal, the ex-Mossad chief insists, although it won’t necessarily dissuade Tehran from making trouble elsewhere. Halevy also emphasizes that no mythical “better” deal would ever win support from Russia and China, Iran’s main weapons suppliers, whose leaders have endorsed this agreement.

In short, both of these top former officials believe the agreement with Iran will enhance their nation’s security – and contrary to what Fox News Channel’s sages might claim, they represent mainstream opinion in Israel’s military and intelligence circles.

So perhaps we can safely discount the partisan demagogues and feckless opportunists who claim to be protecting the Jewish state from Barack Obama. And when someone like Mike Huckabee – who memorably escaped military service because of his “flat feet” – denounces the president for “marching Israelis to the oven door,” let’s remember the sane and serious response of Israel’s most experienced defenders.