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A couple of years ago I was talking to a political science professor about districting, and he said that in districts that are a majority Democrat, they tend to be quite strongly Democrat (I think he said they tend to be 70 to 80 percent Democrat), while Republicans tend to only hold their districts with a 55 to 65 percent majority. I could be completely wrong on those numbers, though, I haven't looked at any data, and the conversation was a long time ago.
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Thinking on these lines, I would suggest that this is not a bounded network, but a multi-level network. It isn't just about influence within Congress as a building, it is about controlling voting behavior within Districts. If even 10 percent of a district is Tea Partiers who will not vote for a moderate, then a moderate Republican would have to do whatever it takes to appeal to them, including vote down a budget.
Just some early morning thoughts before my cup of coffee though. I may change my mind in twenty minutes.