Saw an intriguing article on mediation and the government shutdown:

http://www.washingtonpost.com/business/mediation-key-to-resolving-labor-disputes-divorce-battles-why-not-the-government-shutdown/2013/10/10/f1847b6a-317e-11e3-ad00-ec4c6b31cbed_story.html

I am actually surprised a mediator has not been brought in, yet. A talented mediator might be able to help the parties find mutual interests. The use of a neutral could help diffuse heated emotions. Another benefit would be that both sides might be more willing to listen to a suggestion if voiced by the mediator, even if they would reject the idea out of hand from the opposition.