There is also a rule in the Senate called "cloture". The cloture rule requires a miminum of 60 votes to bring a potential law to the Senate floor for a vote. Any senator has the ability to speak for or against a particular bill, and continue debate on it, until one side or the other votes to cut off debate, and bring the matter to a vote.
You've often heard the term "filibuster", and it's used when a senator threatens endless debate in order to keep an item from vote. If the majority leader doesn't believe he has the votes to cut off debate, he will then table the bill, which in turn, kills it. It requires a vote of three-fifths of duly appointed Senators to end debate.
There are exceptions to the cloture rule, and they usually involve appropriations bills, or bills coming out of joint conference committees (ironing out differences between House and Senate versions of the same bills). Presidential nominations for cabinet posts, judges, and justices, along with treaties, face cloture rules.
The Senate has a set of arcane rules, seemingly out of touch to a lot of folks.