Left/Right spectrum - absolutely. That's why modern spectrum is 2-dimensional, and I totally for expanding it into 3rd and further dimensions:
http://en.wikipedia.org/wiki/Political_spectrum#Other_multi-...
That doesn't mean that we can't more or less precisely place one or the other political force onto it.
This is not "real" science of course, more kind of art, but if we conform to the rules of the game ("liberal democracy" it is called), then I think by polling large enough pool of political scientists/commentators/pundits/whatever-you-wanna-call-them we can arrive at pretty good consensus of where to place one party or the other at each moment in time, wouldn't you agree?
now to your questions:
1. What are the ideas of "real" members of the Left that Obama and the other Democrats are failing to represent?
the link to the article by J.K.Galbraith I gave above perfectly answers it, I think:
Whether your prime interest is housing, health care, peace, justice, jobs or climate change, if you are an activist in America you have known for a long time that this President is not your friend.
2. Since Obama and the Democrats clearly are in opposition to the American Right, what are those ideas that they (the DEMs) are fighting for in opposition to the Right?
Well, I'm actually not even so sure anymore that Obama is in clear opposition to "American Right" whatever that may be. I don't recall any issue during his presidency where he has stood his ground and haven't bowed to pressure from GOP, do you? Guantanamo, Afganistan, Healthcare, Bush Tax Cuts extensions and now Debt Ceiling deal. Not one of those went by unmodified by Tea Partiers, even when Democrats had supermajority.
So I clearly side with commentators who called Obama centrist right from inauguration. I mean, who even calls Obama leftist besides Tea Partiers?