Anbar is not an oil-producing region, though pipelines transport 1.5 million to 2 million barrels of oil through the province daily. But violence in the region still affects markets, said Seth Jones, an associate director RAND Corp.'s International Security and Defense Policy Center and a former senior adviser to the U.S. Special Operations Command.
"This is not the area where most of Iraq's oil fields are located, but instability in general in Iraq and the perception that there could be a civil war may affect energy markets," he said.
Jones was quick to say he believes an outright civil war in Iraq is unlikely, but he and others who spoke to CNBC said that chaos in Anbar could inspire other groups that are already unfriendly to al-Maliki's government and Shiites in general—especially the Kurds in Iraq's oil-rich north—to become restive themselves.
"The worst-case scenario is for the Kurds to say, 'OK, enough of you guys. We don't want anything to do with you. All non-Kurds out'," said Farouk El-Baz, a research professor at Boston University who served as adviser to the former Egyptian government of Anwar Sadat. "They can do that. They have the resources. They have a lot of oil. Then the Kurds in Iraq and Turkey and Syria will all fight for their own nation."