THE BARBARIC murder by the Islamic State of a captured Jordanian pilot has had the effect of galvanizing the Sunni monarchy, which joined the U.S.-led military campaign last summer but faced opposition to it at home. With broad public support, King Abdullah II is now vowing an all-out campaign against the terrorists. But he still has a problem: The United States has failed to deliver promised military equipment, including smart bombs, night-vision gear and spare parts for planes.

The king is not alone in his frustration. Iraq Prime Minister Haider al-Abadi also has said promised U.S. deliveries of weapons have been slow to arrive. And leaders of the Iraqi Sunni tribes that are the foundation of a strategy to restore order in western Iraq say they, too, lack the weapons and ammunition they need to fight. “We’ve received positive messages regarding supplies,” says Ahmed Abu Risha, the president of the Iraqi Awakening Council in Anbar province. “But we didn’t see any results on the ground from the United States yet.”

Mr. Abu Risha and other Iraqi Sunni tribal leaders visited Washington recently to plead for help in recapturing their territory — cities like Ramadi and Fallujah that were taken over by the Islamic State last year. They were received cordially, including by Vice President Biden. But the reality remains that the Obama administration’s plan for constructing a force that can drive the Islamic State out of Anbar remains under-resourced and, in some crucial respects, stalled.

U.S. trainers are working to rebuild Iraqi army units in the hope that an offensive to retake Anbar and the city of Mosul could be launched in a few months. Even if that effort succeeds — and Mr. Abadi’s comments cast doubt on the progress being made — some force must be available to take control of the Sunni populated towns. The Iraqi army, which is predominately Shiite, cannot play that role, which is why the Obama administration has been pushing for the creation of a new civil guard which would allow fighters loyal to Mr. Abu Risha and other local leaders to be empowered and brought under the Iraqi government’s umbrella.

The problem is that legislation to create the guard has yet to pass the Iraqi parliament; Shiite leaders are reluctant to grant authority to the Sunni tribes. Meanwhile, ammunition and other gear promised to the Sunni tribesmen is not getting through, for much the same reason. Mr. Abadi, who is praised by Mr. Abu Risha for his conciliatory steps, has nevertheless failed to bridge the divide. He has also failed to establish the government’s authority over Iranian-backed Shiite militias, which, with no supply problems, are retaking ground from the Islamic State, sometimes with U.S. air support, and then imposing their own sectarian rule.

In his Senate confirmation hearing, Defense Secretary-designate Ashton Carter said red tape had often frustrated prompt delivery of U.S. arms supplies and vowed to tackle the problem once he is on office. That’s welcome, but the trouble in Iraq appears to be more than a bureaucratic blunder. Festering political problems in Baghdad have not been addressed, and President Obama’s commitment of resources and extended timeline for action are simply inadequate. As Mr. Abu Risha told us: “The longer [Islamic State] is in Anbar the more dangerous they will be.”