No Secdef Cheney?

[Hyperbolus]

Former senator John Tower http://en.wikipedia.org/wiki/John_Tower , (of Tower commission fame) was George H. W. Bush' original nominee for secretary of defense, but was voted down 47-53 amid ethical difficulties. House minority whip Dick Cheney was mooted as a replacement and handily approved.
We all know how that ended.
I'm guessing Cheney leaves Congress for the oil industry earlier, and perhaps spends the rest of his career there. Would the H W Bush administration or Gulf War have differed notably; would any butterflies alter Bush' re-election prospects?'