America was founded on the basis of classically-liberal ideals: individual rights, private property, meritocratic rule, as well as an on-again off-again relationship with free capitalist markets. Thus, liberalism is the default setting for American politics and philosophy, and all political leaders/movements must pay fealty to this reigning ideology. Whereas in Europe liberals (and later the socialists) had to contend with the feudalistic aristocrats, who still maintained power in a number of European countries (Great Britain, Prussia, Hapsburg Austria, etc). Also, the reigning two-party apparatus plays a role; the social democratic program of industrial regulations, trade unions, and social welfare was adopted by the Democratic Party during the New Deal (the GOP still holding to classically-liberal ideas on fiscal and economic policy), thus preventing the rise of a contending socialist/social democratic party and effectively co-opting the social-democratic platform under the "liberal" mantra. It's funny cause before the New Deal, the Democrats were traditionally associated with white-ethnic populism and conservatism (with their Southern base), while the Republicans were favored as more socially and economic progressive (at least after the Civil War).
It's helpful to note how the ideologies that rivaled/contended with "liberalism" shaped the movement's identity on both continents. In Europe the classical liberals (and later the socialists) had to deal with the feudal conservatives, who held significant power in most European countries (France being the only meaningful exception). Eventually the liberals compromised on certain issues in order to gain representation. America, on the other hand, never had this clashing dynamic; liberalism monopolized the political discourse, and modern "liberals" are associated with the more social-democratic wing of the movement whereas modern "conservatism" arches toward traditional classical liberalism (along with large doses of traditionalist morality and the imperialistic "neoconservatives").



