Read other letters about this article
Biden's response was directed at, and followed, this statement from Palin:
No, of course we know what a vice president does, and that's not only preside over the Senate -- and we'll take that position very seriously also; I'm thankful that the Constitution would allow a bit more authority given to the vice president also, if that vice president so chose to exert it, in working with the Senate -- and making sure that we are supportive of the president's policies
Article I, Section 3, Clause 4
The Vice President of the United States shall be President of the Senate but shall have no Vote, unless they be equally divided.
No provision for Palin's perceived "expanded powers" in the Senate here. When Biden referred to the VP being in the Executive he was shooting down Palin's (and Cheney's) wet-dream of control of the Senate, and he was quoting the section of the Constitution that laid out the limits. He didn't do it in the clearest fashion, but he was correct. There are no provisions in Article I for "more authority" for the VP in the Senate.