How goes the war against the Islamic State? A useful barometer is the position of Iraqi Kurdistan, which is the most reliable U.S. ally in the battle — and holds the longest front against the terrorists. Four months ago, two senior Kurdish officials traveled to Washington to deliver some dire warnings: The Islamic State was still expanding, no military force in the region could stop it and Kurdistan itself was no longer willing to be part of a shattered Iraq.

Last week the Kurds, back in town for another round of lobbying, could cite some big changes. U.S. airstrikes beginning in August have stanched the threat of an Islamic State offensive overrunning Kurdistan’s capital, Irbil, and allowed the recapture of some key ground. Iraq has a new government with the Kurds’ participation, and negotiations have begun in Baghdad on settling long-standing sectarian disputes.

Yet the bottom line, as the Kurds see it, is this: The Islamic State is still entrenched in a third of Iraq and Syria, still has the ability to carry out conventional military offensives and terrorist attacks and grows more dangerous the longer it keeps its sanctuary. Worse, the prospect that it will be defeated by the U.S.-led coalition as it currently exists is slim.

“We have an international coalition, but the coalition is still in the sky,” said Fuad Hussein, chief of staff to Kurdistan President Massoud Barzani. “We need a coalition on the ground. On the ground we Kurds are alone.”

U.S. and Iraqi officials might call that hyperbole. Iraqi army forces are also fighting the Islamic State in western Iraq and reportedly managed to recapture the strategic Baiji oil refinery last week. Still, Baghdad’s army remains weak and fragmented, with few reliable units. It is still flanked by independent, Iranian-sponsored Shiite militias not under the central government’s control.

A plan to recruit and train Sunni tribesman for a new national guard remains just that, Hussein pointed out. “This is a good idea,” he said. “Maybe it will become a plan. But who is going to implement it? And how can you create a national guard on territory that is currently being held by (the Islamic State)?”

The big political change since the summer is the willingness of the Kurds to give Iraq’s central government another chance, or at least to postpone open steps toward independence. In July the Kurdistan administration insisted it would go forward with a referendum on the territory’s future and balked at U.S. pressure to participate in a new “unity government” in Baghdad. That was before the Islamic State’s offensive against Kurdistan, the beginning of U.S. airstrikes and the Obama administration’s success in forcing the departure of Iraqi Prime Minister Nouri al-Maliki.

Now Hussein says, “We are part of this Iraqi government, and we hope it succeeds.” He added: “We will never give up our right to self-determination. But our priority now is to destroy ISIS (the Islamic State).” The Kurds recently dispatched a delegation to Baghdad and struck a preliminary agreement with the new government of Haider al-Abadi on Kurdish oil deliveries to Baghdad in exchange for overdue budget payments.

Like the army, however, the reconstructed Iraqi central government exists mostly on paper. Festering issues concerning Kurdistan — including whether it will be allowed to export its own oil, whether it will retain control over the city of Kirkuk and on what terms its 150,000-member army will become part of an Iraqi national guard — remain unresolved. The gulf between Abadi’s Shiite party and Sunni leaders remains even wider.

In the end, the Kurds still see themselves as alone. The thrust of their lobbying in Washington was to obtain U.S. heavy weapons for delivery to Irbil, with or without Baghdad’s consent. The Pentagon’s response was grudging: There is a plan in the works to deliver 250 armored vehicles to Iraq, of which the Kurds would get 25. The administration meanwhile plans to train nine Iraqi and three Kurdish brigades, in the hope that will be enough to go on the offensive in northern and western Iraq. But U.S. officials still insist that any arms deliveries to the Kurds go through the central government.

Like many U.S. military experts — including former Defense Secretary Robert Gates — the Kurds see that plan as underpowered. “Three divisions is 10,000 fighters,” Hussein said. Mosul, the declared seat of the Islamic State’s caliphate, is a city of more than 1 million people, heavily fortified with captured U.S. weapons. “Who is going to liberate Mosul?” Hussein asked. “We cannot do that without heavy weapons — Apache helicopters and Humvees, artillery, rockets, sniper rifles.”

“To liberate Mosul, we need an army with us,” said the Kurd. “Where is that army going to come from?” That’s a question the Obama administration has yet to answer.

Jackson Diehl is deputy editorial page editor for The Washington Post, where this column first appeared.