President Obama spoke at the United Nations Wednesday to rally the world to combat the Islamic State, and he sometimes sounded like a Nobel Peace Prize winner mugged by reality. That's the good news. He said the world is a "crossroads between war and peace; between disorder and integration." In the best passages he called on Muslim nations and leaders to counter "the lethal and ideological brand of terrorists who have perverted one of the world's great religions."

Alas, this realism was leavened with Mr. Obama's familiar calls to good intentions, the promise of "collective" defense, and false confidence that the tide of history inevitably turns toward peace and harmony. Sorry, but history is made by men and nations, and the failure to grasp that in his first six years is why he is now having to fight another war in Iraq and into Syria.

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Meanwhile, a threat to U.S. security that Mr. Obama didn't mention is unfolding in Yemen, where on Monday Iran-backed Houthi rebels seized most of the capital city of Sanaa, leaving hundreds dead and dictating the terms of surrender to the U.S.-allied government. This is the same Yemen that the President has called a model for his counterterrorism in Iraq and Syria.

The Yemen government's collapse comes after Houthi protesters paralyzed the capital for weeks, ostensibly to demand the restoration of fuel subsidies that the government slashed over the summer. Government attempts to meet the protesters halfway failed, and on Sunday Houthi gunmen swept into the city. A U.N.-brokered ceasefire is supposed to provide more Houthi representation in government, but the rebels are refusing to disarm.

The Houthis—members of Yemen's minority Shiite Zaidi sect—now control 14 of Yemen's 21 provinces. They've inherited a broken economy, a bankrupt government, and a long-running battle against al Qaeda in the Arabian Peninsula (AQAP). This is the same battle the U.S. has been fighting as part of a semi-covert effort using drones, CIA agents and special forces working with Yemeni soldiers.

Whether the U.S. can continue this fight is now in doubt. Though Shiite grievances against Yemen's Sunni majority are an old story, the Houthis—named after their late commander Hussein Badreddin al-Houthi, who was killed a decade ago—are a more recent creation. Formed in 1994 as "the Society of Young Believers," the group is vociferously anti-American and has longstanding ties to Iran's Revolutionary Guards Corps, which has supplied it with arms and military training. Houthi fighters have in turn fought for the Assad regime in Syria.

This week Iran has loudly refused to join the coalition against the Islamic State, so don't expect a Houthi government in Yemen to work with the U.S. against AQAP. The Houthis may want to wage their own war against AQAP, but there's a limit to their reach, especially in the country's largely ungoverned south. Before ISIS emerged, AQAP was the jihadist group posing the most serious threat to the U.S. homeland.

What is likely is a dramatic expansion of Iran's role in Yemen and its proxy war against Saudi Arabia. "A phenomenon more colossal than Lebanon is unfolding," Alireza Zakani, an Iranian parliamentarian known to be close to Ali Khamenei, said Monday, referring to Iran's de facto control over much of Lebanon through Hezbollah. "After the victory in Yemen, surely it is Saudi Arabia's turn."

That may be bluster, but it gives a sense of Iran's regional ambitions. Much of the world's oil goes through the Bad-el-Mandeb strait separating Yemen from Africa, just as it goes through the Strait of Hormuz separating Iran from the Arabian peninsula. Having a reliable client in Yemen would give Tehran influence over both waterways to stretch U.S. naval resources.

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Saudi Arabian forces bombed Houthi positions in late 2009, and Riyadh sent its troops into Bahrain two years later to prevent a Shiite uprising against the island's Sunni rulers. Given the Kingdom's nervousness about its own Shiite population in its eastern province, it will not easily acquiesce in a Shiite-dominated state on its southern flank.

The Saudis might feel they must intervene, and an expanded conflict could become a humanitarian and strategic calamity. The lesson of the Syrian war is that unchecked disorder begets unchecked fanaticism, which inevitably draws America in. While the Saudis have a large military, it isn't clear it could defeat Houthi forces hardened by years of battle and supplied by Iran.

The Obama Administration failed to oversee a peaceful transition in Yemen. Our options are now diminished, but at a minimum we can insist that the Houthis lay down their arms as a precondition to participating in government. If they refuse, the U.S. may have no choice other than to help the Saudis help the legitimate government regain power. The alternative is ceding another chunk of the Mideast to an Iran that is dedicated to becoming a nuclear power.