Having ignored Iraq since 2009, the Obama team is now desperately trying to devise a way to prevent its total collapse — and to roll back the jihadi state newly established on a third of Iraqi territory.

The only slim hope of doing either requires the ouster of the leader whom the United States has backed for nearly a decade, Iraq’s paranoid prime minister, Nouri al-Maliki.

Maliki’s sectarian Shiite politics have driven Iraq’s Sunnis — a fifth of the country’s population — into the arms of the Islamic State movement (known as ISIS). This jihadi group recently seized control of the country’s second-largest city, Mosul, and declared a “caliphate” spanning western Iraq and eastern Syria.

If Maliki stays, he may trigger a regional Sunni-Shiite holy war that threatens America’s Mideast allies. His presence will attract more foreign fighters to join an estimated 3,000 Europeans and dozens of Americans already training inside the so-called caliphate.

Iraqi Kurds, Sunnis and two of the major Shiite parties now oppose him. Even Iraq’s Grand Ayatollah Ali Sistani has signaled it’s time for Maliki to exit. Yet the Iraqi leader insists he will serve a third term.

Having squandered its influence in Baghdad, Washington has little leverage left to help ease Maliki out.

Maliki was a problem from the time the United States first backed him as a compromise choice for prime minister in 2006. When I asked Iraqi politicians back then to describe him, they repeated the phrase, “Dawa, Dawa, Dawa,” meaning he retained the conspiratorial mindset developed in the underground Dawa party of Shiites that fought Saddam Hussein for decades. Maliki’s inner circle consisted of aides from Dawa with the same limited outlook.

While he briefly adopted a more inclusive outlook, he had begun a systematic campaign to seize control of the army and the state by 2009. By 2010, the gains of the U.S. troop surge — when Sunni tribes turned against al-Qaida in return for promises to include them in the bureaucracy and in Iraqi forces — had been squandered. Maliki reneged on those promises and arrested thousands of Sunnis.

He also placed cronies in top command positions in the Iraqi army and strengthened Shiite militias. These actions precipitated the army’s recent collapse in Mosul and convinced Sunni tribes to back the Islamic State.

In late 2010, Maliki even threatened U.S. officials in a meeting in Baghdad, saying he would restart a Shiite insurgency in southern Iraq if they failed to back him for a second term. I was told this by Ali Khedery, a U.S. official who served as a special assistant to four ambassadors in Baghdad and also to Gen. David Petraeus.

Belatedly, the White House realizes they backed a destroyer. Secretary of State John Kerry has now made two quick trips trying to encourage Iraqi politicians to choose a prime minister who would reach out to alienated Kurds and Sunnis. Although Maliki’s party won a plurality in recent elections, it would be possible to oust him if other parties, including Kurds, Sunnis, and some Shiites, united behind another candidate. So far the parliament has been paralyzed, but it will meet Sunday to try again.

Although the odds are awful, what would it take to persuade Maliki to leave?

First, it would require the full engagement of Obama and Kerry, and the application of all remaining U.S. leverage to help mediate an alternative to Maliki. Kerry should make clear that no U.S. planes or air support will be forthcoming to such a sectarian prime minister. As Petraeus put it recently, the United States “cannot (become) the air force for Shia militias.”

Second, Iran would have to accept a Shiite alternative to Maliki (the Iranians are the key political operators in Baghdad). This would make rational sense for Tehran, since the collapse of Iraq, and the emergence of a Sunni jihadi caliphate, threaten Iranian interests. But the debate said to be ongoing in Tehran about whether to dump the Iraqi leader has apparently not been resolved.

Third, Iraq’s Kurds, Sunnis, and many Shiites would have to realize that the “partition” of Iraq is no solution. “We will not fall apart in three neat pieces; it would look more like Somalia,” says Feisal Istrabadi, the distinguished former Iraqi diplomat who is now a professor at the University of Indiana Law School. Kurds would be threatened by the Islamic State; Sunnis and Shiites would be dragged into bloody conflicts with each other and within their own communities, as militias proliferated.

This may be the disaster toward which things are headed. But the White House must at least try to head it off.