As the world's attention this past month has been on the valiant defense by Kurds of the Syrian border town of Kobani, ISIS forces in Iraq have been gobbling up Anbar province in Iraq and now, according to the Chairman of the Joint Chiefs, General Martin Dempsey, the terrorists are threatening Baghdad itself.

Haaretz:

“I have no doubt there will be days when they use indirect fire into Baghdad,” said Gen. Martin E. Dempsey, President Barak Obama's top military adviser, said in an interview on ABC's "This Week." While he doubted the Islamist militants would make a direct attack on Baghdad, he did say he expected fighters from the Islamic State, also known as ISIS and ISIL, to infiltrate areas near the capital.

According to the New York Times, the Islamic State has already carried out suicide bombing attacks in Baghdad.

The adviser also said that fighting the Islamic State would remain a "very challenging task" until the Sunni population of Iraq becomes convinced the government represents its interests.

“The government of Iraq, which is moving but has not yet achieved a narrative that would cause the 20 million Sunnis who live between Damascus and Baghdad to believe that their future is with the government of Iraq, in the case of Iraqis, and certainly the Syrian regime is not reaching out to the Sunni population in Syria,” Dempsey told ABC News’ Martha Raddatz for “This Week.”

“Until those facts change, this is going to be a very challenging task. In other words, until ISIL doesn’t have, you know, freedom of movement in and among the populations of Al Anbar Province and Nineveh Province, and in Eastern Syria, this is going to be a challenge,” Dempsey said.

General Dempsey acknowledged the challenge on the ground and said during "This Week" that the U.S. had to bring in Apache helicopters to bail out Iraqi forces when Islamic State fighters were within 20 to 25 kilometers of Baghdad's strategically important airport.

“Had they overrun the Iraqi unit, it was a straight shot to the airport. So we’re not going to allow that to happen," he said. "We need that airport.”

Dempsey said Islamic State fighters are adept at concealing themselves from air attacks, blending in with the local population.

“The enemy adapts and they will be harder to target,” said Dempsey. “They know how to maneuver and how to use populations and concealment. So when we get a target, we’ll take it.”

Might IS forces overrun Baghdad? As our defense of the airport showed, Islamic State cannot mount large scale assaults without being cut to pieces by our air power. Until or unless IS can develop adequate anti-air defenses, we will almost certainly be able to keep them from taking Baghdad.

The Iraqi army defending Baghdad may run, but there are tens of thousands of fanatical Shia militiamen who would defend the city to the last. And it's believed that several hundred Iranian Revolutionary Guards from the crack Quds unit are also in Baghdad to stiffen resistance.

But IS can cause a lot of trouble for the Iraqi government. Daily suicide attacks are raising the civilian body count and as Dempsey points out, they could eventually be in position to lob a few mortar rounds into the central city spreading even more panic.

The battle for Baghdad is more a psychological struggle than a military one. And as with most everything having to do with Islamic State, they hold the upper hand.