Many things that the Republican party says and does strike me as far-right.
I'm not sure if I can bring up specific issues without this thread turning into a political mud fight, but the UK Conservative party is mostly OK about climate change being a real thing, abortion and gay marriage. Even their worst-case dismemberment of the NHS would be far more socialist than "Obamacare".
On the economic side of things, it seems that America tends towards classical liberalism (i.e. conservatism), for it lacks any kind of social democratic or socialist thought. When is the last time you heard a major American party call for something to be brought into public ownership?
But this is exactly my point. While it seems to me that there are very few on the left in the US, I am but one data point. Right and left, liberal and conservative are completely meaningless as descriptions of anything.