The Obama administration continues to insist on maintaining the unity of Iraq. Meanwhile, back in the real world, the Sunni extremists of ISIS are on the march. On Sunday, ISIS seized three towns in northwest Iraq from the Kurds and threatened to overrun the Mosul Dam, a key source of electricity and water for much of the country. At the same time, ISIS forces crossed the border from Syria into Lebanon, taking control of the city of Arsal, blindsiding officials in Beirut.

The three-year revolt against Bashar Assad in Syria has morphed into a regional crisis with sectarian conflict at its core. The political structure of Iraq has exacerbated that crisis.

Iraqi Prime Minister Nuri al-Maliki is a Shiite chauvinist with close ties to Iran. In the six years of his rule, he has destroyed the fragile bonds of trust between Shiites and Sunnis that had developed during the Sunni-led effort in 2006 and 2007 to expel al Qaeda from Anbar Province. After ISIS routed the Iraqi army in June this year, Mr. Maliki unleased Shiite militias linked directly with Iran to stabilize the front line north of Baghdad.

Beginning in 2011, Mr. Maliki attacked Iraq's Sunni vice president, Tariq al-Hashemi. and the Sunni finance minister, Rafi al-Issawi, on unsubstantiated terrorism charges, driving Mr. Hashemi into exile and Mr. Issawi into hiding. Now Mr. Maliki's suspicion of the Sunnis has taken on clinical dimensions.

Convinced that Baghdad is honeycombed with Sunni sleeper cells readying themselves to support an ISIS assault on the capital, he has empowered the Shiite militias to conduct security sweeps inside the city. The New York Times has reported that last Friday one of these militias abducted Riyadh al-Adhadh, an important Sunni politician who heads Baghdad's provincial council. The militiamen also seized and his bodyguards and beat them from midnight to sunrise in an unsuccessful effort to force them to admit that their boss was helping the insurgency. After being freed through the intervention of a militia leader, Mr. Adhadh declared that "we are living in a jungle."

Reflecting on the chaos created by multiple militias, a young man in Mr. Adhadh's neighborhood told the New York Times that "Iraq requires another leader like Saddam Hussein, who's like an official murderer." One doubts that this young man was familiar with Max Weber's definition of the state as a human community that "successfully claims the monopoly of the legitimate use of physical force within a given territory," but he certainly got the gist of it. By that standard, Iraq has ceased to be a state.

In the aftermath of April elections, the glacially slow Iraqi political process has finally produced a Kurdish choice for president (a largely ceremonial post) and a Sunni for speaker of Parliament. The Shiite parties are supposed to agree by Friday on a nominee for prime minister.

That may not happen. Although reconciliation with the Sunnis is inconceivable if Mr. Maliki remains prime minister, it won't be easy to move him aside. His party constitutes more than one quarter of Iraq's Parliament and more than one half of the Shiite bloc. Unless he decides to stand down, the parliamentary stalemate will continue. Even if he can be persuaded to leave, recent history suggests that it will take months for party leaders to decide on the final shape of a new government. ISIS is unlikely to hit the pause button while the Iraqis haggle.

It is time for the Obama administration to ask itself some hard questions.

The first question is immediate and urgent. Although Mr. Maliki has ordered the Iraqi air force to assist the Kurds in their battle against ISIS, he remains adamantly opposed to U.S. military assistance for the Kurdish government. If American arms could help the Kurds repel ISIS, does it make sense to hold these shipments hostage to Mr. Maliki's fears of Kurdish independence?

More broadly, why should the U.S. continue to resist Kurdish independence—for example, by blocking their efforts to sell oil on the world markets? Even if another Shiite politician replaces Mr. Maliki, a Shiite-led Iraqi government will always be beholden to Iran for the sustained assistance it needs. It is hard to discern the justification for pressing the Kurds to maintain their allegiance to such a government. We are noticeably short of friends in the Middle East, and an independent Kurdistan in what is now the Kurdish part of Iraq would be a natural ally.

Finally, isn't it time to rethink our basic assumptions about the Middle East? Multiethnic democracy is a noble ideal, but it doesn't seem feasible in current circumstances. For the remnants of the Ottoman Empire, the real choice lies between large multiethnic countries or large countries devolved into smaller political entities, each dominated by a single group. The former seem more likely to yield either dictatorship or anarchy; the latter offer at least the possibility of non-oppressive self-government.

There is nothing sacred about the post-Ottoman state system in the Middle East—and no good reason why the U.S. should continue worshiping at its altar.