http://www.senate.go...s/pdf/RL30945.pdf
"The Vice President of the United States is the SenateÂs official presiding officer
(formally, ÂPresident of the SenateÂ), as provided in Article I of the Constitution"
And this:
"Since the SenateÂs official presiding officer is not a member of the body, the
presiding officer position does not have the same powers to control floor proceedings
as those held by the Speaker of the House. The SenateÂs presiding officer may speak
only if granted permission to do so by the unanimous consent of the membership, and
he may vote (as noted above) only to break a tie."
So no, the VP has no power to influence the Senate
due to his position as the President of the Senate. Is he able to work with senators? Absolutely. As can the chief of staff, legislative aides, lobbyists ... Point is, being the President of the Senate grants exactly one power: the tie-breaking vote.
"... do believe that Palin would have, more than any other VP in modern history, spent time in the Senate oversight role ..."
What oversight role? I'll answer for you: there is none.
And ... what evidence do you have of this belief? "... as part of his effort to "clean up Washington" ..."
Is that it? Because you believe that working closely with the Senate is necessary to clean up Washington, that must be what she was referring to?