Percolation problems are common in condensed matter physics, and the percolation paradigm -- the idea that a fluctuation or a cluster or a subgraph is big if it threads the entire system -- is an immensely useful way of thinking about problems. (See here for an explanation of how the vulcanization of rubber is a percolation process.) Apparently even Republicans appreciate this paradigm -- see this story about four young Republicans on a roadtrip across the US that never leaves a Republican district. Much as I approve of the attempt, 1. it's fairly obvious that you can do this; just keep away from cities. 2. it's a recipe for excruciating boredom even if you're a young Republican.
(Neither Obama nor McCain has a very good shot at percolating through the US in November. Obama's just totally fucked from this perspective, but McCain just might win Oregon in which case he'd percolate with ease.)
Update. USA Today has some county-wise maps from 2000 and 2004. It's trivial for McCain to percolate countywise, and impossible for Obama.
Further update. Josh Patashnik at The Plank discovers that the college Reps are not in fact percolating. Apparently they couldn't take the tedium. Understandable, but very weak.