The Congress usually does not hire mediators to settle budget of other parliamentary disputes. The process usually involves direct debate between Congressmen and Senators on the floor, with the Speaker taking on the role of a facilitator. Mediation is usually not part of this process.
However, given the length of the current stalemate and the urgent nature of the decision at hand, Governor Dayton proposed the idea of using a mediator to settle the current budget dispute. An interesting move indeed. Though it was rejected today, it might be representative of the fact the mediation is becoming mainstream as a tool in resolving disputes quickly – in almost any situation. Not just the traditional labor disputes, business disputes, Employment disputes, Etc. but new arenas such as legislative issues, sovereign issues involving negotiations between countries, or between international bodies such as the IMF or the United Nations and one or more countries. The North-South Sudan peace negotiations are a good example. Turkey might end up being a mediator in establishing Palestine a sovereign state.
Though such cases have always been around, their frequency and media visibility appears to be highlighted in recent years.