>For starters, I thought most stuff was done on a 2/3 majority basis, so I wasn't really sure why one man changed much.

Nope, simple majority. Exceptions include passing new amendments or overriding presidential vetos. I believe that these need a two-thirds majority.

>Another thing is that I thought all senators voted independently (if they voted in parties the President could surely do what he liked, as there wouldn't often be the necessary 2/3 majority veto) so why does it matter too much if one senator defects?

Although all Senators do vote independently, votes are oft times divided along party lines. This isn't to say that every vote thus far has been 50 for and 50 against. If you break down the "ayes" and "nays" and cross reference them with Republicans and Democrats, you'll see that a lot of Republicans generally vote one way and a lot of Democrats voting the opposite way.

It's all statistics, anyway.

-Faux "hope that helped" Pas