The issue convulsing this country, and splintering its governing coalition, is not a nuclear-armed Iran or a moribund peace process. It is the question, as wrenching as it is unique to the Jewish state, of whether the country’s fast-growing ultra-Orthodox population should continue to be exempt from compulsory military ­service.

The debate came to a head this week, with Shaul Mofaz’s announcement that his Kadima party would quit, after a scant 70 days, the broad coalition assembled by Likud Prime Minister Benjamin ­Netanyahu.

Likud retains a majority without the centrist Kadima, although one now torn between religious parties resistant to weakening the exemption and ultranationalists demanding an immediate draft for both ultra-Orthodox and Arabs.

But the real threat is to Israel’s prospects, not Netanyahu’s. How the uproar over service is resolved will shape the nation’s economic and social future.

Strangely, this is a matter on which Likud and Kadima essentially agree. They agree, as well, that the exemption, declared unconstitutional by the Israeli Supreme Court and set to expire Aug. 1, must be substantially pared back.

The argument is over the scope and pace of change, and the ramifications of adjusting either too fast or too slowly.

Too fast, warn Likud and its allies, and the ultra-Orthodox will stage an ugly revolt that will cleave Israeli society.

“The integration of the ultra-Orthodox into Israeli society is of enormous importance. The question is how you do it,” says Ron Dermer, a top Netanyahu aide. “If you pull on the rope too hard, the whole thing is going to snap.”

Too slowly, warn Kadima and its allies, and the revolt will come from a secular majority fed up with being freierim — suckers. They not only serve in the military but pay taxes that support religious schools and fund a social safety net that enables an astonishing 55 percent of ultra-Orthodox men to remain outside the workforce.

“We’re verging on a trajectory of Israel slipping toward a third-world economy, and a third-world economy can’t sustain a first-world military,” says Yohanan Plesner, a Kadima member who chaired a committee to rewrite the exemption. “I see this as no less than an existential threat.”

The roots of today’s controversy date to Israel’s founding in 1948. In the raw aftermath of the Holocaust, Prime Minister David Ben-Gurion agreed to excuse students in yeshivot (religious schools) from military service.

Then, there were 400 such students. Now, the number has soared to 40,000. The ultra-Orthodox — known as the Haredim, those who tremble before God — make up about 10 percent of the population. More significantly, one-fourth of Israeli first-graders come from Haredi families observing the biblical commandment to be fruitful. With an Arab population of 20 percent, and growing quickly, the burden of service — allowed but not mandatory for Arabs — will fall increasingly on the secular population.

The argument is nominally about military service; it is about much more. The military exemption is contingent on ultra-Orthodox men continuing to study, making them unable to work legally. Meantime, their separate, state-funded schools offer scant preparation for decent jobs; secular subjects such as math and science are not taught to boys after eighth grade. Currently, 60 percent of Haredi families live in poverty.

This situation is unhealthy and unsustainable. Low workforce participation by Haredi men — and Arab women — “will not only result in a further increase in poverty but also undermine Israel’s overall growth potential and fiscal sustainability,” the International Monetary Fund warned recently. Bringing the ultra-Orthodox into the military would offer a glide path for integrating them into regular society.

This assimilation is, from the ultra-Orthodox perspective, precisely the problem: the threat of losing youth to the lure of secular life. Some extreme elements are anti-Zionist; others believe they serve the state, and protect troops, with Torah study and prayer. The more pragmatic recognize that more service is inevitable, but they want to postpone the day of reckoning as long as possible, to age 23 or even 26 instead of the usual 18.

A walk around the ultra-Orthodox neighborhood of Mea Shearim underscores the Haredi sense of being under siege from modernity, with wall posters in Hebrew warning of the dangers of the iPhone and inveighing against forced conscription.

From the American vantage point, this argument seems remote and esoteric. But its continued festering matters to the United States because it is so crucial to Israel’s future strength. And the failure of the short-lived national unity government to forge a solution is, consequently, bad news for both countries.