DB9
Very well known Exeweb poster
Think the closest the Democrats get to the Labour Party is Bernie SandersThe Nazi party weren't left wing. They may have used 'socialist' in their title but it wasn't an ideology they agreed with, it was a simple appropriation of the term for political capital.
As for American politics, they don't compare to ours. America doesn't really have a left wing as such. The Republicans are probably somewhat right of our Conservatives and the Democrats somewhat akin to middle of the road Conservatives. They'd have a complete fit if anything like Labour existed as a main political party.