There is isn't a whit of substance in anything the VP can do - it's just acting as the moderator. He can be overruled by the Senators if they don't like the way he applies the rules (there have been many cases of that over the years), which makes his theoretical power in reality completely illusory. Nobody has pointed to anything Cheney has done to influence the course of debate or success/failure of proposed legislation using his "powers" as presiding officer, other than his tiebreakers, averaging less than once per year over the entire Bush/Cheney era. Biden was right that the only substantive power the VP has, and the only thing that can't be overruled, is tie-breaking. Biden has spent decades speaking, offering motions, debating, using procedural tactics, and voting in the Senate; Palin, in contrast, has zero experience in the Senate, and famously remarked a few months ago that she didn't know what the Vice President's job is. If you think she knows more about how procedure works in the Senate, then your partisanship has outstripped common sense.
You might have been referring to Thomas Jefferson, who wrote a manual for how to run parliamentary debates two hundred years ago. That's an 8th grade bit of knowledge. It's a nice little work, and like Roberts Rules of Order has some legacy value, but it is not the Senate Rules. The Senate makes and adopts those itself, and has a Rules Committee to propose and consider new rules and amendments (the V.P. is not on that committee, or any other committee for that matter). The committee that put together the September, 2007 revision to the Standing Rules was:
COMMITTEE ON RULES AND ADMINISTRATION
DIANNE FEINSTEIN, California, Chairman
ROBERT C. BYRD, West Virginia
DANIEL K. INOUYE, Hawaii
CHRISTOPHER J. DODD, Connecticut
CHARLES E. SCHUMER, New York
RICHARD J. DURBIN, Illinois
E. BENJAMIN NELSON, Nebraska
HARRY REID, Nevada
PATTY MURRAY, Washington
MARK L. PRYOR, Arkansas
ROBERT F. BENNETT, Utah
TED STEVENS, Alaska
MITCH MCCONNELL, Kentucky
THAD COCHRAN, Mississippi
KAY BAILEY HUTCHISON, Texas
C. SAXBY CHAMBLISS, Georgia
CHUCK HAGEL, Nebraska
LAMAR ALEXANDER, Tennessee
There's no Cheney in that list, because he isn't entitled to be on it. The V.P. doesn't even attend committee meetings for any of the committees, where much of the real work of the Senate takes place. He often doesn't attend the general sessions.
If your biases make you want Biden to be a dummy about the Senate where he's worked for decades, and the self-professed hockey mom to be a legislative procedural genius, you're entitled to those views. I'm tired of arguing that the world is not flat, and invite anybody else to have the last word.
See you all in the air; I'm back to flying topics.