An informative essay by Josh Chafetz on the Constitutonal role of the VP:

But the thing is, our Founding Fathers created a system in which the vice presidency went to the Electoral College runner-up. And even though they didn't anticipate the role that political parties would come to play, they knew enough to understand that this meant that the president and vice president might well be rivals. As a result, the Constitution gives the vice president no executive role at all, other than waiting for the president to die, resign, or become incapacitated. Indeed, John Adams, our first vice president, wrote to Abigail that "[m]y country has in its wisdom contrived for me the most insignificant office that ever the invention of man contrived or his imagination conceived." The Founders didn't think that the executive role of the vice president would be flexible; they thought it would be almost non-existent.

Biden, however, kept mangling away. "The Constitution is explicit," he said. "The only authority the vice president has from the legislative standpoint is the vote, only when there is a tie vote." Well, not exactly. The vice president is always the president of the Senate--indeed, since the vice president was expected to have so little an executive role, presiding over the Senate was meant to be his day job. As Roger Sherman put it at the Philadelphia Convention, "If the vice president were not to be President of the Senate, he would be without employment." Biden was therefore right to note that the vice president's Senate vote is limited to breaking ties, but wrong to think that this constituted the entirety of his responsibilities with respect to Congress.

This was also a funny line: "Skipping over Biden's assertion that Cheney 'has been the most dangerous vice president we've had probably in American history' (a bit of hyperbole is forgivable in the midst of a campaign, but is Cheney really worse than, say, the dueling and possibly treasonous Burr?)...."