Somewhere else, I took a mental ax and sliced capitalism into its most basic components:
http://archives.econ.utah.edu/archives/pen-l/2007w51/msg00055.htm
If I'm right, then opposition to the horrific forms of extra-economic appropriation that modern capitalism has enabled (e.g. 19th-21st century imperialisms) and gross social inequality (on which capitalism rests) belongs in the left, even if that opposition falls short of opposing markets in general.
I still believe with Marx that markets are responsible for the fragmentation and mystification of social life, for pitting people against people. But I think that the distinction has some validity, since capitalist markets are markets premised on gross inequality, and some of the worst consequences of markets result from the broader social conditions on which markets exist. This by the way, Marx noted explicitly in Grundrisse and Capital.
But aside from that, I don't think the workers of their world are ready to abolish markets for the time being. Gross inequality "of opportunities" and private enrichment by appropriation of the natural environment, the commons, public funds, (some forms of) technology, information, etc. are totally or much more exposed. There is not a widespread collective need to abolish markets as there is to abolish privilege, corruption, etc.
So, in my view, "conscious opposition to capitalism" thus qualified encompasses a lot of people in the U.S. But, even if one preferred a narrower definition of the left that included only those opposing capitalism toto, including the "principle" of markets, even that narrower group of people -- I think -- is today at a different place, politically, than they were in the 1990s.