I think any chance of Bush winning a second term went out the door once Lee Atwater passed away in 1991.
The second term went out the door when he broke his tax pledge. The entire party opposed this, including all the good soldiers who sucked it up and tried to defend the decision publicly. Bush was virtually the only man in the GOP who believed the Democrats would honor their half of the deal. Sheer folly, but Bush flattered himself that he had risen above partisanship.
It went out the exact moment when a reporter asked about his reversal on his no new taxes pledge and he dismissively said "Read my hips."