Maybe you could fire a rocket in the opposite direction the whole time, but that increases fuel requirement even further.
Of course, if you followed the landing, you know that things didn't quiet go as planned, and Philae bounced a few times (and almost escaped the gravity), so this is definitely a difficult problem, but I suspect that once you have a lander that can anchor itself enought to not bounce, you could probably anchor yourself enough to drill.
[1] "I feel," "It seems," etc. - I don't have the maths or the physics to back this up beyond intuition and a hasty free body diagram sketch, which admittedly seems to work well-ish for most problems in classical mechanical physics.
The Earth's gravity on your body enables all this force; without it you need to invent some other way of pushing down the drill.