The length constraints at the NYT were rather strict, but the longer version is here.
UPDATE: A reader forwards this Senate history of the Vice Presidency. Click "read more" for an excerpt.
Here's the excerpt:
Several framers ultimately refused to sign the Constitution, in part because they viewed the vice president's legislative role as a violation of the separation of powers doctrine. Elbridge Gerry, who would later serve as vice president, declared that the framers "might as well put the President himself as head of the legislature." Others thought the office unnecessary but agreed with Connecticut delegate Roger Sherman that "if the vice-President were not to be President of the Senate, he would be without employment, and some member [of the Senate, acting as presiding officer] must be deprived of his vote."
Under the original code of Senate rules, the presiding officer exercised great power over the conduct of the body's proceedings. Rule XVI provided that "every question of order shall be decided by the President [of the Senate], without debate; but if there be a doubt in his mind, he may call for a sense of the Senate." Thus, contrary to later practice, the presiding officer was the sole judge of proper procedure and his rulings could not be turned aside by the full Senate without his assent.
The first two vice presidents, Adams and Jefferson, did much to shape the nature of the office, setting precedents that were followed by others. During most of the nineteenth century, the degree of influence and the role played within the Senate depended chiefly on the personality and inclinations of the individual involved. Some had great parliamentary skill and presided well, while others found the task boring, were incapable of maintaining order, or chose to spend most of their time away from Washington, leaving the duty to a president pro tempore. Some made an effort to preside fairly, while others used their position to promote the political agenda of the administration.
Biden -- and Chris Matthews and other flacks -- have made fools of themselves on this issue, by not only pretending it's settled that the VP is purely Executive, but by pretending that anyone who says otherwise doesn't know anything. It's true that in practice the VP has morphed into a kind of junior co-President, but as I note in the Northwestern University Law Review article linked above, that's a political change that's probably unconstitutional. You'd think Biden would at least read the Senate website. . . .