I heard the Senate rules require that at least one member of the opposite party must be present.
untrue... They need a quorum (generally assumed to be 60% or 3/5 of all house members). The 3/5 rule applies here as is written in the bylaws for the WI house (or whatever they call it - it is analogous to a state house of reps). They have 19 R members and 14 D members. 3/5 of 33 is 19.8, or 20 members as a practicable number.