Iraq's military is not capable of rapidly counter-attacking ISIL:
[Chairman of the Joint Chiefs of Staff General Martin] Dempsey said the Iraqi army had “stiffened” its resistance to a fast-moving insurgency led by the Sunni fighters of the Islamic State of Iraq and Syria, which has renamed itself Islamic State and declared a caliphate on land it controls. He said government forces were “capable of defending Baghdad” but added that they would be challenged to go on the offensive without external support. ...
“In any military campaign, you would want to develop multiple actions to squeeze” Islamic State, Dempsey said. “You’d like to squeeze them from the south and west. You’d like to squeeze them from the north and you’d like to squeeze them from Baghdad.”
Although I worry that ISIL sleeper cells in Iraq (if they exist in any numbers) could make Baghdad a bloody battlefield, I'm pretty confident that the Iraqi government can hold the capital and points south.
While I think that Iraq could manage to slowly plow their way north (and west for that matter, at Fallujah and the rest of Anbar), it would be costly in Iraqi troop losses and civilian casualties.
I've noted that the Iraqis need a core force of trained troops to move quickly on offense and deliver precision firepower, the way the French led the offensive against al Qaeda in northern Mali. Lesser quality Iraqi troops would follow in their wake to garrison and hold terrain.
I suggested the Jordanians--who I noted sent mechanized troops to their border--could be the core force to advance east from Jordan toward Ramadi and Fallujah to help the Iraqis restore control of the main road to Jordan. Since Jordan is viewed as a potential target of ISIL, it makes sense for Jordan to preempt that threat.
I suggested the Kurds, too. While I doubt that the Kurds would send troops to the Baghdad front, if the Kurds advanced on Mosul in the north, it would help cut off ISIL troops on the Baghdad front. Since we are sending an assessment and planning team to the Kurdish region, too, I suspect this will happen.
The Iraqis could launch their more ponderous attacks north and west mostly to fix the ISIL forces in place while far to their rears, Jordanians rally anti-ISIL Iraqis in Anbar and Kurds rally local Sunni Arabs who don't want to live under jihadi rule.
The Iraqi government might even be able to manage their own core force that can spearhead a drive north. While their counterattack on Tikrit has not been setting land speed records in the Middle East, using helicopters to push troops into ISIL areas was gutsy and has potential.
With our advisers present in all of the offensive forces to call in our fire support and help with logistics, we could kill a lot of jihadis trying to hold their caliphate before they give up that objective and scatter.
Dempsey noted a major problem in using fire support, but one which indicates a good thing--we have to be careful about calling in firepower because pro-ISIL targets are mized with anti-ISIL Sunni Arabs. That problem has kept the Iraqis from forcefully attacking in the Fallujah region all year. But the debacle in the north is likely to make the Iraqis think of just killing them all and letting Allah sort them out, as they bombard their way north.
We can help restore the situation despite letting it deteriorate to this extent. Work the problem.