It does not remain rock steady on its axis but wobbles. This wobble is normal. There are factors that influence this wobble such as the changing distribution of mass at the surface: melting glaciers, shifting ice sheets, and yes pumping massive amounts of ground water up to the surface (the estimate was something like 2 trillion tons). I've skimmed through a number of scientific sites that have stated scientists have noted the drifting along Earth's polar axis (31.5 inches eastward) and are tracking it. They have stated that the amount of drift in comparison to the size of the planet will not produce any noticeable changes to life on Earth. In fact, according to NASA the farthest the rotational pole has drifted away from its average position since modern observations began is 37 feet. Earth will not flip topsy turvy nor will it flop onto its side. The only thing this is going to cause is the need to adjust our GPS systems.