Yes, it is the genomic DNA that is causing you trouble. Although a brief 1000g spin should bring it all down, the pellet is never tight and you almost always are going to pull up some gunk with the clear supernatant. A better solution is to include a quick sonication step (5-10s) before the 1000g spin. That way, the DNA is sheared and it should pellet better. It has worked for me most times. Also, remember to use a reasonable volume of SDS buffer when you lyse the cells. Too little buffer and its always going to be hard. For comparison, I use about 200ul per 1ml culture pellet and this volume works well for both pre- and post-induced cells.