Actually, no. He didn't give him the benefit of the doubt nor did he think Saddam would straighten up. He was very confident that the regime was destabilized enough to allow the Shia (south) and kurd (north) uprising to remove him from power.

Stormin' Norman made a tactical error in the cease fire agreement that allowed Iraq to use military helicopters. This was supposed to be to allow for travel since all the roads and bridges were taken out, but Saddam immediately supressed the Shia uprising ... killing close to 10K Shia in the processes. Same in the north with the Kurds. As soon as we realized what was going on we started the no-fly zones. but by then, it was too late. Saddam had regained his hold over the state.

Bush 41 really thought Saddam was done-for and so we didn't need to do anything else.