I trust you'll permit me to address your question about the differences between the Left and Liberalism on another occasion (a separate post), so suffice to say for now I think it has to do with how "politics" itself is conceived (hence the truth of your remark that 'the general debate about the nation's health speaks volumes about our politics') and how the economy and "marketplace" are conceptualized as part of the "private" sector. Relatedly, Liberalism lacks the conceptual resources to sufficiently restrain capitalism and overcome the pride of place accorded economistic values. In short, "capitalist democracy" is conspicuous for its capitalism insofar as it is allowed, in the end, to define both the character and structural contours of democratic theory and practice. Yet to think of capitalist democracy as "separate 'parts' is to miss the vital integrity of the system" (Joshua Cohen and Joel Rogers), a system that finds philosophical warrant and ideological blessing in the form of Liberalism. Thus Liberalism can countenance the formal granting of political rights but is often blinded to inequalities in the distribution of resources that decisively affect the exercise of such rights (cf. the recent SCOTUS decision in Citizens United). Furthermore, we have what Cohen and Rogers term a "demand constraint:" "As a result of their control of investment, the satisfaction of the interests of capitalists [qua capitalists] is a necessary condition for the satisfaction of all other interests within the system."
With regard to the workers you cite above, their welfare "remains structurally secondary to the welfare of capitalists, and the well-being of workers depends directly on the decisions of capitalists." Here, the ideological rhetoric of the Right (e.g., when it talks of the 'special intersts' of unions) captures an essential truth of Liberalism inasmuch as it must live with the fact that "the interests of capitalists appear as general interests of the society as a whole, the interests of everyone else appear as merely particular, or 'special.'"
I could say more here but Cohen and Rogers do it better in their little book, On Democracy: Toward a Transformation of American Society (1983).
Mind you, I'm in many respects still a "Liberal" (especially of the Millian sort*), hence it is possible and quite likely, in Dick Flacks' words, that one might "be a Marxist in the morning, a pacifist in the afternoon, an environmentalist at dinner, and a feminist in the evening, while going to church on Sunday and voting Democrat on election day."
The Left, generously defined, is sensitive to the limits of the Liberal tradition, and in transcendence of those limits it need not abandon such things as the value accorded moral autonomy or the importance, say, of constitutionalism as found in that tradition (any more than my identification with the 'religious left' means I need turn my back on the progress enshrined in the European Enlightenment). **
Again, forgive me if I postpone a deeper treatment until another day.
*On the "Millian sort of Liberal," please see Kwame Anthony Appiah's The Ethics of Identity (2005).
**On the perils of "anti-liberalism," especially those of "communitarian" provenance, please see Stephen Holmes's The Anatomy of Antiliberalism (1993). For some of the reasons the Left should embrace much of the Liberal tradition, see also Holmes's Passions & Constraint: On the Theory of Liberal Democracy (1995). Gerald (Jerry) Gaus also articulates many of the reasons the Left should cherish its Liberal heritage.