Within that majority, there are three or more factions, now testing their influence and even sinking legislation. Has there ever been a more daunting impasse?

This is not an uncommon problem in life. There are many things that require a consensus in order to be accomplished. Think of software, for example. Open-source platforms like Wordpress need constant change in order to stay ahead of trends. It's a platform anyone can contribute to changing, but only the best code survives. Changes are made by consensus. 

Or Wikipedia. The need for consensus is obvious. There has to be something on the main display page. The editors who are most interested in a particular topic tend to prevail and this is probably as it should be. It is not a perfect system. Marginal views get pushed aside often. But there is a paper trail and everyone is in a position to evaluate rule compliance. Most of the time, the results are very good.