To add to
rpl's writeup, the reason a filibuster can last past one person's
endurance is because the Senate floor is controlled by the Senator who is speaking. The speaker can
cede it to another Senator of his/her choosing; thus, during a
Democratic filibuster,
Barbara Boxer might end her stint with "I cede the
floor to the honorable gentleman from
New York" (
Charles Schumer), and Schumer can begin speaking in opposition to the
bill, or reading the
phone book (
Strom Thurmond did this during the filibuster
P_I mentioned), or saying anything he wants to say as long as he keeps talking.
A cloture vote to forcibly shut a speaker up requires a 3/5 supermajority, or 60 votes.