Cheney has been called impeachment insurance on the theory that however bad/hated the Democrats think Bush is they think Cheney is worse and the thought of Cheney in charge will keep them from trying to remove Bush. But would Cheney really be any worse of a President than Bush? Cheney’s been highly involved in the administration since he took office, I can’t imagine that his policies would be all that different from Bush’s.
This doesn’t really answer your question, but i think what freaks most people out about Cheney is that he’s the first VP in at least half a century who shows no signs of ever wanting to be president, and is thus exempt from playing politics and showing a good side. Whereas every past VP in my lifetime (and presumably long before) had to make an effort to keep up appearances, and even Bush does this to some degree, Cheney flat out doesn’t care. He just says whatever he wants, which baffles most people. He’ll say things that directly contrast Pentagon reports or curse out senators on the floor with no regard for decorum.
Would this actually make him worse than Bush? Hard to say. But with Bush there’s at least the illusion that he’ll sit down and have a dialog with the opposition (especially now the the opposition has some teeth). Trying to reason with Cheney seems more like shouting at a brick wall.
Could this be because Cheney is more interested in power than prestige, and as (arguably) the most powerful VP in history, he’s already achieved his aims?
At least one Republican insider claims that Cheney actually does much of the deciding for the “decider”:
Invasion of the Party Snatchers by Victor Gold
If the assertions made in this book are true, then there would indeed be very little difference between a Cheney presidency and what we’ve seen thus far from Bush (and, interestingly, a Bush presidency might have looked considerably different, given a different VP.)