They might have been anomalous, but it is pretty clear that the only way the movement for civil rights was able to seal the deal was because the state stepped in and upheld the judgment of the court, bypassing the mainly reactionary (and democratic) wing of the legislature. Likewise most of the labor rights that were won in the early part of the twentieth century. State legislatures may have some progressive potential, but on the whole democracy qua voting in the US (at least since the Constitution) seems to trend more in the direction of Woj's cynical description, even if he overstates it a bit.
However, I think this is a weak understanding of what democracy means.
Democracy as voting is likely more conservative in the US (with exceptions), but democracy in terms of people pushing for change in the street has had some effect (the teabaggers being no exception to this rule). Sometime the latter has also been progressive in some ways. When you have a conservative executive or court, there is less likelihood that a democratic push could have any progressive effect (pace Doug's pal Daniel Lazare); in that circumstance, when there is also no real progressive democratic push, there is no chance.
Of course, there is also the fact that little progressive change (except possibly in some areas of minority rights) has taken place since the fall of the USSR, i.e. it is difficult to say whether the internal trend towards progressive change wasn't part of a larger conjuncture. I don't know enough about the USSR to say anything about whether it was a good thing for the people in the country itself, but at least the idea of an alternative seemed to provide some umbrella for more progressive change in the USA. If you look at the two watershed moments of progressive change here--the 1930s and the 1960s--it seems pretty clear that the options for political change were at least tinted by the threat of Communism*.This seems to be an important factor often left out of pronouncements about US politics like these.
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* I'll bracket the Civil War since there is some debate about the internal colonialism of the North to the South, which somewhat colors the idea that it was all about slavery--a whole other can of worms. Jim Crow was democratic in the sense that the people who were able to vote helped to institute it; it was upheld by the courts, but that didn't make it any less popular.