Obviously the possibility of 'finishing the job' was dicussed, and rejected, by the US. The Gulf War was fought by a coalition of nations, [u]under a UN mandate that did not authorise removing Saddam Hussein from power[/u].

As Rask has pointed out, the Americans get spit on if they don't act, and they get sh!t on if they do. I wouldn't blame them a bit if they decided to 'go it alone' and simply flattened Bhagdad, with or without UN approval.