Interesting discussion...... Here's what the Constitution says, Art. 1, Sec. 3, para 4:
The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.
The following is the Riddick Senate Procedure.... Go down to page 1219 to the section: Change in, Power to make and it gives a detailed discussion of the changing rules in the Senate.
http://www.gpo.gov/congress/senate/riddick/1217-1228.pdf