This leads to an interesting question, although outside the scope of the current WI.
What if Bush doesn't refer to the Axis of Evil in his 2002 State of the Union?
I don't think there's much point trying to make him leave Iran out of the Axis; once the phrase exists, Iran is in. However, a quick Google suggests that it was coined by a speechwriter who'd been instructed to make the case for attacking Saddam, and became enamored of the analogy of Iran and Iraq as a modern day axis. So what if the writer just concentrates on Iraq and Saddam? Maybe a further conentration on the crimes against his own people? Saddam as a Hitler of the Middle East? A mad dog who has attacked Iran, Kuwait, and his own citizens, and needs to be stopped before he lashes out against somebody else? No threat to Tehran that they're next, as soon as Saddam has had his account settled. Iran and the US keep working together on picking up fugitives fleeing Afghanistan? I'm not convinced that this unoffical partnership will ever see an open rapprochement, but the butterflies from not being actively antagonistic towards Iran appear to be absolutely enormous when 2003 rolls around.