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I think this is mostly a problem with our elected officials, and not so much with the citizens. I think most poeple are actually seated IN the aisle, and elected officials stake out extreme positions left or right to pander to their most active constituents. Most people are closer to the center and would welcome some compromise to deal with some of our problems, but as you said, our elected officials are too far apart to compromise.
But what I mean is that when you attempt to homogenise society across great demographic oceans, you will find that the variation in the will of the people becomes ever greater. Not everyone is standing in the aisle, I suppose in some ways perhaps many are. But on issues such as the legalisation of cannabis and war, for example, people are pretty divided. My solution is to decentralise power on most issues, retaining centralised control over security and the environment, perhaps for starters. Let the people decide over the smaller issues, allow for a more tribal structure on the smaller scale. For example, if some don't want people in their neighborhood smoking pot, then they can fuck off and live in a different town, and vice versa, problem solved! Then everyone is happy. Yeah I know of course I fail too see the bigger picture, it's not going work, not now anyway, people are too stupid. Like I said though is require everyone to have an open mind, and few people have in todays world.
The thing about centralised governments is that they fail miserably to address any kind of problems that come up, because the system does not allow them to. They are responsible for causing many of the problems in the first place and they attempt to patch things up by introducing more ineffectual laws, which in turn only exacerbate the problem further.