I think much of the problem with our current system (and has been seen in the "Occupy" movement as it has grown) is that it doesn't take into account the hard wired limit in our brains when we try to interact with more than about 150 people (as discussed by Malcolm Gladwell in "Tipping Point" for example). Our "representatives" are not accountable or responsive.
My own experience with juries (I have served on four now) is that it is a system that really does work the vast majority of the time. I have found that people who serve on one are not exactly happy to do it, but they understand why they need to, they understand the stakes and consequences, and are generally very conscientious. I would much rather stake my freedom or even my life on the jury system rather than one based on a judge alone. If you have served as well, you may well agree with this point. If so, why does that democracy work and our broader one not? I think a big reason is the rule of 150.
Why not organize at the lowest level in groups (neighborhoods) of no more than 150, then that group selects one representative to serve at the next level of government also limited to 150 representatives, and so on to a third level (which would represent in total no more than 3,375,000 people - roughly equivalent to a state). At each level, the rule of 150 is preserved so that people could actually get to know one another and at least have a chance to work together. Accountability is baked in. Provide a "bill of rights" to ensure the inviolable ones are preserved. Establish the scope of authority so that the first level takes care of neighborhood issues, the second level schools, local roads, zoning, etc. The higher level groups would be unauthorized to establish rules that are within the scope of the lower level (something important that was completely lost in our system somehow).
It would at least be better than the system we have now.