IMPEACH CHENEY IF YOU WANT, but do bear in mind that he'll preside over his own impeachment trial.
No, really. The Senate has the sole power to try impeachments. The Vice President is the President of the Senate. He presides. The Constitution provides for only one exception in cases of impeachment: "When the President of the United States is tried, the Chief Justice shall preside." That's because of the obvious conflict-of-interest of having the VP preside when the President is tried. But there's no similar provision for having someone else preside if the Vice President is impeached.
Presumably that's because no one could imagine a Vice President doing anything significant enough to warrant impeachment, which was certainly an accurate reflection of the office's character for the first two centuries or so of our nation's history. And it's another argument against the VP being given extensive executive responsibilities, now that I think of it.