| In the United States, and probably among any people around the world who were conscious in the 1960s, this term has a much different meaning.
It refers to a loosely united group of radicals -- mostly student radicals -- who were looking for a brand of politics that was much more committed than the namby-pamby liberalism that was afoot then. At the same time, they saw some of the perils of Soviet-style Communism and rejected it.
Remember that a lot of the original New Lefters were people who had literally put their lives on the line in the civil rights struggle down South. They'd been gassed, hosed, beaten up etc. by Southern officials. They'd seen compatriots killed.
Yes, it's true that as the Movement aged, some factions moved closer to more orthodox styles of Marxism -- whether that be Stalinism, Maoism, whatever. But the movement started out with a healthy disrespect of both Soviet and capitalist systems.
The New Left described in the original post seems much more akin to the group of politicians in the United States that we refer to as New Democrats, a group that includes Clinton, Gore, et al. | 
