The median Republican Congressional district now has a population density 11 times smaller than the median Democratic district[.]
Chart from here, which goes on to explain:
As shown in the chart above (in Log scale), there was a relatively strong positive correlation between density of congressional districts and the vote share of the Democratic candidate in the 2010 elections. Of densest quartile of districts with a race between a Democrat and a Republican — 105 of them, with a density of 1,935 people per square miles or more — the Democratic candidate won 89. Of the quartile of districts with the lowest densities — 98 people per square mile and below — Democratic candidates only won 23 races.
This is a pretty intense urban-rural divide. Shifts like those in Colorado which transferred rural Congressional Districts 3 and 4 from Blue Dog Democrats to Republicans no doubt made it more intense.
If you wanted to be more fine grained in your analysis, I also have no doubt that intraparty liberal-conservative divides would also show a meaningful connection to population density: moderate Republicans probably tend to be from more urban districts, while conservative Democrats probably tend to be from more rural districts.
I also suspect that further analysis would show that if you were took take more fine grained data, for example, census tracts, that average population density in a district would match the partisan split even more strongly. In other words, it is possible to have a large Congressional district in which most of the voters live in a densely populated central city or two, and a minority of voters live in outlying areas around the cities that house most of the people in the district. My expectation is that geographically large Congressional Districts in which most voters are crammed into central cities but there are large, barely populated outlying areas are more liberal than geographically large Congressional Districts with a steady low level of population densities (e.g. districts that have only small towns, rural areas and exurbs).
There is a credible argument that population density is indeed one of the prime drivers of partisan identity - that living in an urban area causes Democratic policies to make more sense, while living in a rural area causes Republican policies to make more sense.
One way to test that would be to look at changes in political ideology upon moving from an area that has high population density to one that has low population density and visa versa. If an individual's politics get more conservative when he or she moves to the country, and more liberal when he or she moves to the city, then the case for population density causing political identity would be supported (although one could also argue for neighborhood effects that are independent of population density in that scenario).
It is possible to argue for causes other than population density for this divide. For example, one could argue that it is farming, rather than population density that drives it. But, this would fail to explain why exurbanites are more conservative than outer ring suburbanites who in turn are more conservative than inner ring suburbanites who are in turn more conservative than central city residents, none of whom are involved in the farm economy. A population density explanation can also explain why cities like Columbus, Ohio, which have a large land area for their population, are more conservative politically than more densely populated cities like Denver.
One important caveat is that I am not at all sure that this relationship holds in all U.S. regions. In the South, partisan divides based on race and religion may swamp most population density effects, while in the North, I suspect that racial and religious divides merely reinforce the population density effects. There are many rural blacks in the South and few in the North.