Bush Sr probably thought that if enough Iraqi decided they didn't want Saddam ruling the place, then the people could change the regime- it's not like this hadn't happened before in other countries.
Also it seemed like a possiblity in recent war, that with an obviously superior army was going to roll through the place, that the regime could collapse. Again, it didn't happen.
I still don't fully understand how this regime managed not to collapse even when it was "all over". I think part of the answer lies in the unability for people to speak- due to a system of terror that was widespread- but I don't think this was the whole story. Another part of the story I think was the disconnect between the people and those in control- the people weren't important- they were window dressing for an organization existed on oil revenues.
It still doesn't make much sense, and it will be interesting to get the whole story.