Is a liberal Christian simply a Christian who is politically left-leaning? Is it more than that? Which is more important to the person -- that they're liberal or that they're Christian? Or to frame it in Andrea Dworkin's term -- what is they're "identity of primary emergency"?
I can only answer for myself. But having communicated with and read work by others who either explicitly or implicitly bear the title of "liberal Christian," I think my personal answer can be readily generalized.
While I try not to identify my political stance with any party, I am certainly politically liberal. In many ways, however, my political stance derives from my theology. I am not liberal in one sphere and Christian in another (you can tell I'm Lutheran, huh?). Rather, I am liberal BECAUSE I am Christian. So to answer one of the questions above, my identity of primary emergency is Christian.
Another question above, however, is still unanswered. Am I a liberal Christian simply because my politics are left-leaning? No. Ignoring politics, I am still a liberal Christian. Liberal here points to much more than politics. It points to my theology as well. To illustrate this, it may be important to examine the liberal/conservative dichotomy through a different, non-political lens.
In many situations, "conservative" refers to a desire to either maintain the status quo or to return to a past model (either historical or imagined). "Liberal" refers to the desire to change the status quo to a model yet to be realized. It is through this dichotomy that I identify my theology as Christian. I am not comfortable with a Christianity where homosexuals are damned, all sex is limited to marriage, war as crusade is justified, the poor are oppressed by an ethos that views their failure as the desert for their effort, etc.
My theology is forward looking in the same way that Jesus's ministry on Earth was. I am a liberal Christian because I believe our current world is not good enough. We can change it for the better by aiming for a target that is in the distance. On the horizon. A target on the border between the present and the future.