You get some nut elected in 1992 with a relative liberal like buchanan as VP after Dukaki's one term.
Of course even if the no new taxes pledge wasn't given, Bush almost certainly rehearsed it aloud and the Democrats could somehow get a recording of said rehearsal and use it against the Republicans in 1992 thereby ironically helping Dukaki get reelected. Even thinking about making a campaign promise that had no hope for delivery is a big no-no.