The VP as presiding officer of the Senate can stop debate and votes if there is no quorum present and can rule debaters out of order if they stray from the proposition at hand....like slipping ammendments into bills that haven’t been debated, etc. It’s all in Robert’s Rules and could be a full time job if she wanted it instead of the stooges that act as President-Pro Tem.
I don’t have the specifics handy, but I have read that Thomas Jefferson, who was VP when John Adams was president, had an active understanding of the VP’s role as president of the Senate. By the way, I think Jefferson would have been happy to see Palin come along, who well fits his ideal of the citizen politician.