Obviously, air strikes via fighter jets launched from the USS George H.W. Bush seem likely, but fighter jets (in this case the F-18 Hornet) are expensive to replace and the pilot's life is at risk if enemy ground forces have managed to procure any effective means of air defense. On board the USS Philippine Sea are Tomahawk cruise missiles. These cruise missiles can travel hundreds of miles before reaching their intended target and they cost roughly $1,000,000 a unit versus $60,000,000 per F-18. Coincidentally, Tomahawk missiles first made media headlines during Operation Desert Storm in 1991 when the coalition forces defeated Saddam Hussein's Iraqi army in Kuwait. Should the US decide to assist Iraq with air strikes, it would make more sense if they opted to use cruise missiles initially.
As of now, the US has still not made a decision regarding the use of air strikes in Northern Iraq.