One, they need a facilitator who is truly non-denominational, who can cut them off when they talk too long, and keep moving towards something actionable. The biggest problem with this, of course, is that the folks in Washington seem convinced that there is no one worthy of such a task because they've got the monopoly on wisdom.
Two, they need to move from talking to modeling their assumptions. If a congressperson wants to plan lunch, he talks. If he wants to plan a campaign trip for next month, he talks. If he wants to change health care for the biggest economy in the world, he talks. Compare communication with transportation. If that same congressperson wants to go to lunch, he walks. If he wants to go to a function across town, he drives. If he wants to go back to his district, he flies. He uses different technologies for travel but not for communication and planning. It's no wonder that Congress doesn't get anywhere - it is still doing the planning equivalent of walking everywhere.
Imagine a session in which a facilitator (or two) captures the assumptions that these politicians are making. "You are saying that liability insurance drives doctors out of rural areas. Okay, what is the causation and what is weighting? Liability of more than what triggers an exodus from rural areas?" And bit by bit, the model could be constructed. Then, the causation could be tested. Data that exists could be used. Data could be collected. Assumptions could be tested and collected into a network of causality and then simulated. Technologies exist for this. As the group works on this, a few things would happen. Leverage points would emerge. It may well be that the objectives of covering everyone and holding down costs could be met with a far less comprehensive plan. And the group would gradually be brought together over a model that is grounded in data.
Finally, such an approach might just do something to disarm the ideological who resist practical solutions because of principles. And on that note, an excerpt from Dietrich Dorner's wonderful book, The Logic of Failure: Recognizing and Avoiding Error in Complex Situations, in which he's talking about the success people have with systems simulations.
“The good and bad participants did not differ … in the frequency with which they developed hypotheses about the interrelation of variables in Greenvale. [That is - we all develop our theories about how the world works.] Both the good and bad participants proposed with the same frequency hypotheses on what effects higher taxes, say, or an advertising campaign to promote tourism in Greenvale would have. The good participants differed from the bad ones, however, in how often they tested their hypotheses. The bad participants failed to do this. For them, to propose a hypothesis was to understand reality; testing that hypothesis was unnecessary. Instead of generating hypotheses, they generated ‘truths.’”