The Progressives are absolutely a liberal party, not a socialist party; ensuring workers' control of the means of production has never been an end in itself for the party, just a means to ensure greater freedom. (At times, they even come down against it.) It's just that Anglo-American liberal thought has never been big on laissez-faire and has always had quasi-socialist undercurrents; compare Smith, Paine, JS Mill or Lincoln to their European equivalents and you'll see what I mean. The British Liberal Democrats and their Commonwealth equivalents have just moved from principle to pragmatism after fifty years of electoral dominance; they're the splitters, not us. In the US, you just can't have right-wing liberalism.
As for conservatism, it could never have held any national sway in most of the US to anywhere near the degree that it does in Europe or elsewhere because there's quite simply no base for them outside of a few weakening regional strongholds. They can't rail against foreigners or deviants effectively; the US has a fairly open culture that has historically been good at assimilating ethnic minorities into an American identity. Even the huge masses of former slaves only took a few generations to become indistinguishably "American" everywhere outside of the South, and there it only took a few more. Even the remnants of the Democrats in the South aren't nearly as extreme as the European conservatives about "the looming threat of mongrelization." (I'm sure many of you Europeans remember Rick Perry blowing his stack when the Tories tried to gift him that Obama Golliwog back last year.) The US is also not under direct threat of invasion by anyone like the Communists or the Chinese and doesn't have the bones of an empire to hold down, so there's no support for the kind of hypermilitarism that you see in the European or East Asian countries. The US doesn't have a state church to rally around, so political religion isn't nearly as big (and seems like more of a Socialist thing here anyway where it does exist).
