Christopher Beam tries to answer the question:

Since the election, conservatives have consoled themselves with the idea that Obama may have won, but America is still a "center-right nation." But the phrase is tossed around with little evidence-possibly because there is none. Even if there were evidence, the term is so muddled as to be meaningless.

Read the whole thing. I'd say Beam's problem is his insistence that a political term have some clearly defined meaning. Take the term "neoconservative" for example. Half the "serious" journalists in Washington have no idea what the word means, but we still understand what they're saying when they use it. In the case of describing the United States as a 'center-right nation,' I think it's pretty clear that this must be taken as relative to other countries. Beam's not impressed by that explanation:

Another defense of the C.R.-bomb is to compare the United States with other countries, especially European ones. After all, we're more religious, our unions are weaker, and we tend to favor free markets over government control. But as Ramesh Ponnuru points out on National Review's The Corner, "If that's all it means to say 'center right' … we could probably go through a long period of political domination by liberals and still qualify." Even if we are center-right by global standards, that has little bearing on whom we elect.

Center-right may not have much impact on whom we elect, but it does mean that the elected should steer well clear of the social and foreign policies engineered in center-left European democracies. The American left has a fascination with European social policy and a love affair with international institutions. Conservatives fear both. Of course center-right has little bearing on whom we elect, otherwise we would have elected the center-right candidate. But perhaps conservatives mean this as a warning, as in, even though you won the election, don't try and make the United States into a social democracy with an anti-Israel, anti-democracy-promotion tilt in foreign affairs. Voters won't like it. This is still a center-right nation.