I find that back pain from cycling occurs when pushing too big a gear. Of course, this assumes that the bike is set up properly for you to begin with. Pushing too big a gear usually occurs in seated climbing, so if you can't shift down low enough that you're not "pushing" the gear, climb out of the saddle (standing) more frequently.

I ride a fixed gear bike, and most of my climbing is out of the saddle. I used to have low back pain, but avoiding seated climbing, as well as a morning stretch routine, and discontinuing heavy squats and leg presses in the weight room, and now my back feels relatively fine. (If it feels painful in the morning, the morning stretch cures that.)

L.