When the operation to liberate Mosul started earlier this week, the American commander in charge of the US contribution estimated that it would take at least “several weeks” to accomplish, and likely much longer than that. The Iraqis feel more confident after first contact with the enemy, CBS News reports. Officers in the field have bragged that entering the city — ISIS’ largest urban center and a key strategic point for their survival — would just be a matter of hours rather than days. Iraqi prime minister Haider al-Abadi joined in the enthusiasm, but CBS’ correspondent cast some cold water on some of the claims:

On Wednesday, an Iraqi officer bragged to CBS News that they would be inside Mosul within a matter of hours – a much faster approach to the city where there are thought to be less than 5,000 ISIS militants still holding out.

Even Iraqi Prime Minister Haider al-Abadi was optimistic Thursday, telling a diplomats gathered in Paris to discuss his country’s crisis that the offensive was going “more quickly than we thought.”

“Our forces have started to move forward to free this city which was taken by IS over two years ago. The fighting forces are currently pushing forward toward the town more quickly than we thought, and more quickly certainly than we established in our plan of campaign,” Al-Abadi told the attendees via video link.

CBS News correspondent Holly Williams doesn’t quite see it the same way:

Williams says the reality, however, is that it’s very slow going as the Iraqi troops and Kurdish forces clear these towns and villages, even though most of their residents fled a long time ago.

The terrorist forces won’t fight in the open, which makes progress easy until the military units get drawn into more urban settings. That’s when the carnage will really begin, especially given the fact that ISIS fighters don’t really have an option to retreat. Coalition forces, including US air power, have their sites trained on the western egress routes in order to capture or kill ISIS leadership if they pull out. But even apart from that, these fighters know that a retreat from Mosul will mean an excruciating execution if they manage to make it to Raqqa, and surrender means spending the rest of their lives in prison back in their home countries. They’ve got nowhere else to go, and very soon they will fight like it.

Still, so far it’s good news for the Iraqis, and now they have even more resources to deal specifically with the tactics of terrorists — thanks to the US:

Iraq’s elite counterterrorism unit joined the battle to recapture Mosul from the Islamic State for the first time on Thursday, as Iraqi army forces and Kurdish soldiers attacked the militants’ positions outside the city on several fronts.

Commanders said the counterterrorism force, which has received training and support from the United States, was besieging the town of Bartala, about six miles east of Mosul. Half a dozen Humvees from the unit were prepared to enter as Iraqi forces pounded Bartala with artillery. …

As Kurdish and Iraqi forces have pushed into the network of villages surrounding Mosul, they have found them heavily defended and booby trapped — a situation only expected to get worse as they draw closer to the city.

Iraq’s black-clad counterterrorism troops are among the most celebrated and effective units in the military. They have led the assaults on Ramadi and Fallujah over the past year.

It’s worth noting that the Assyrian Christians in the region came primarily from these outer villages, as did the Yazidis and other ethnic and religious minorities. I spoke with Fr. Douglas Bazi Tuesday on Relevant Radio, and he mentioned that the main city is almost entirely Muslim. The outer villages have been largely abandoned because of the genocides conducted by ISIS, so that may make it even easier to push through them. The question Father Bazi posed was whether the victims of the ethnic and religious “cleansing” will ever be able to come home again, because others seized their homes after they left while trying to distance themselves from ISIS in Mosul. Watch for fault lines in the coalition later, but for now everyone is focused and united on the first task of ridding Iraq of ISIS.