I mean, everyone knows that the Vice President has no day-to-day Constitutional* powers whatsoever. The VP's tie-breaking powers are rarely called upon — Cheney and Gore did it once every year or two. As for assuming the office if the President dies, that hardly counts as something for the VP to "do every day". And that's the end of the list of enumerated powers. As far as I can tell, the only reasonable argument that the Vice Presidency should even exist is that it discourages political assassination by an opposition party that controls the House of Representatives.
Basically, what I'm saying is: I, too, wonder what exactly a Vice President does every day. Modern Presidential administrations have generally crafted a meaningful role for the VP, but it's never been written into law. It seems technically possible to discharge the office of the Vice Presidency while lying on the beach sipping margaritas, waiting for your party to page you for a tie-breaking vote once a year.
There is, of course, the minor matter of that other page, which is the main reason you want someone who's qualified. But if you were a politician who wanted to accomplish things — and especially if you wanted to do so on your own terms, rather than as a surrogate or adjunct for a President with whom you may frequently disagree — it seems entirely reasonable to refuse the Vice Presidential nomination on the grounds that it's a powerless office. Politicians have done it before (most famously Daniel Webster, whose rejoinder "I do not intend to be buried until I am dead" is a favorite of history buffs, and which all politics junkies know nowadays because it was quoted by John Hoynes on The West Wing).
Not that Palin evinces any such instincts. She accepted the nomination.
* The fact that Cheney has unconstitutionally assumed all sorts of other powers is an entirely different matter.