A quick analysis of the U.S. Election in Two Sentences:

The Democrats' mistake was in thinking that their characterization of events and situations would go as unanswered, as unchallenged as it used to -- and miscalculated (when going to them for campaign help) and misunderstood that those on their extreme left were as equally frightening or distasteful to the mainstream electorate as they (the democrats) found the extreme on the right to be.

The Republicans saw, quite correctly, a Left that was blind to international corruption, even showed sympathy for terrorists, while turning over every possible rock to see if they couldnt find some (corruption) of our own, and the mainstream electorate resented the insistance that the Left's self-loathing accurately defines us.

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Actually, the question, as asked:

What did Bush do that made (just) over half of the American electorate vote for him?

Shows a lack of understanding for the US electoral process. We don't run two unaffiliated, random candidates for president. We have a party system. Whoever either party runs is going to get darn close to 40% of the vote, given that our two parties, at this point represent a closely divided country.

The question should be (as discussed here ad nauseum), "How did Bush get the 11% that Dole or Clinton did not get?"