Here is an idea to help Matthew-Y get past his reservations about the utility of impeachment proceedings against Cheney.
Start with the general premise that it would be better, from any number of perspectives (take your pick), that Bush-Cheney step aside. Any corporation would have replaced them after no WMD were found (even though the American public re-elected them, forcing the current constitution crisis).
Whatever the case, Bush-Cheney ought to resign for the good of the nation. Most in their party will agree.
Rather than face continued impeachment proceedings against his VP, Bush appoints Baker, on the heels of Cheney's resignation, according to the 25th Amendment. The Congress accepts Baker, on the provision of Bush's resignation (and that Baker will not become a GOP nominee). Baker, ascending to the Presidency on the heels of Bush's departure, submits a name for the VP, probably agreed upon in advance, formally or informally. Let's say it is Hamilton or Powell (i.e., someone who might get easily confirmed).
Thus, it is not the votes in the Senate or the crass vox populi that is standing in the way of clearing the decks. It is the legacy lust and more of those who refuse to step aside, for the good of the nation.