An annotation on Passage 3373 of James Madison's Notes of Debates in the Federal Convention of 1787 3373


John Adams, the first president of the Senate. Courtesy of the Library of Congress.

The original idea was that a senator would be president of the senate.  However, this led to a couple of problems.  First, if the president could vote only during a tie, the state would be under-represented.  Second, if the president could vote at all times, the state would be over-represented as the senator would have two voting seats. 

To solve these problems, the Brearly Committee decided that the vice president would be president of the Senate. 
Reference: Sidney M. Milkis and Michael Nelson, The American Presidency 55