Supporters of the Islamic State of Iraq and Syria wave al-Qaeda flags in front of the provincial government headquarters in Mosul, Iraq, on Monday . (Associated Press)

As the Obama administration debates whether and how to intervene in Iraq's rapidly unfolding crisis, many advocates of intervention have argued that action in Iraq should be matched by action in Syria. Should the United States actually intervene militarily in support of the Iraqi government, however, it should know that it will be on the opposite side of many of the Arab networks that support the Syrian uprising.

That's not because they support the Islamic State of Iraq and Syria (ISIS), which has been in a state of open warfare with most other Syrian rebel groups. They just mostly don't see ISIS as the primary issue. Many of the most vocal Arab backers of Syria's rebels support what they cast as an Iraqi popular revolution against an Iranian-backed sectarian despot. They equate the Iraqi uprising with the Syrian uprising, as a Sunni revolution against a Shiite tyrant, and actively oppose U.S. or Arab intervention against it. For just one example, the Kuwaiti Islamist preacher Hajjaj al-Ajmi, who has been one of the most prominent fundraisers for Syrian insurgency groups, has urged repeatedly against supporting "the moves by America and Iran to confront the Iraqi revolution."

That seems to be a popular view, at least among those sectors of the Arab public most invested in supporting the Syrian insurgency. The Saudi professor Ahmed bin Rashed bin Said, who tweets to 350,000 followers as @loveliberty, said, "We must support the Sunnis of Iraq not only because they represent the Arab and Islamic face of Iraq, but to save Syria and limit Iran and protect the Gulf." A former Qatari ambassador recently warned that a U.S. intervention on Iraqi Prime Minister Nouri al-Maliki's behalf would be seen as a war on all Sunnis. The Qatari journalist Faisal bin Jassim al-Thani laid out the lines of the new conflict in stark terms: "Hezbollah and the United States and the United Arab Emirates are all in Maliki's trench while the people and the ulema and the honest ones are with the revolution." (The UAE has since withdrawn its ambassador from Iraq, and its officials have struck a decidedly critical tone toward Maliki).

These Arab voices tend to minimize the role of ISIS and instead emphasize the broad base of support for Iraq's insurgency. Ajmi tweeted recently to his 443,000 followers that "what is happening in Iraq is a revolution of the people against injustice and tyranny and combating it over ISIS is meant to give cover to striking the revolution and frustrating it in the name of a war on terror." The popular Al Jazeera personality Faisal al-Qasim recently observed to his 1.5 million Twitter followers that the Syrian and Iraqi revolutions were examples of "dressing up a popular revolution in terrorist clothes, demonizing it and opening fire on it." Former Kuwaiti member of parliament Walid al-Tabtabaie, for instance, supports the "Iraqi revolution" while warning that ISIS "has some good people but is penetrated by Iran" and that "the corrupt in Syria can't be in the interest of Iraq… they will stab you in the back."

ISIS is a real threat, without question, a savvy and experienced fighting organization with a clear ideology, significant financial resources and a proven ability to attract foreign fighters to its cause. But this Arab counter-narrative shouldn't be ignored. The sharp divide between an American debate that focuses exclusively on ISIS and an Arab debate that focuses on a broad Sunni rebellion starkly evokes the similarly skewed discourse in the first few years of the U.S. occupation of Iraq. From 2003 to 2006, U.S. officials and media often reduced the Iraqi insurgency to "al-Qaeda" and regime dead-enders, thus vastly exaggerating the importance of al-Qaeda in Iraq, delegitimating the political grievances of the Sunni community and missing opportunities to divide the insurgency. Heavy-handed, indiscriminate military responses informed by these views helped to fuel the insurgency.

The architects of the "surge" didn't only bring more U.S. troops to Iraq and begin different counterinsurgency practices. They also moved away from such oversimplifications and began to better understand the tribal networks, local politics and diverse armed factions that made up the insurgency. This conceptual improvement then allowed creative commanders, empowered by Gen. David Petraeus's team, to work effectively with Sunnis who had grown disenchanted with al-Qaeda in Iraq. Those "Awakenings" made the decisive difference in Anbar province. Those among the Awakening movement included many nationalist and Islamist factions that had very recently been fighting against the occupation. The United States put many of them on payroll as "Sons of Iraq;" their rough treatment by Maliki after the U.S. departure in late 2011 contributed to their alienation and is part of the deeper background