We need to distinguish between sea ice (a ~1m thick layer of frozen seawater), and land ice (up to 3000m thick layer of compacted snow). Sea ice is quick to respond to climate change (because it's so thin), and has a large seasonal component to its extent. Land ice is much slower to respond, and harder to replace once it's gone.
Antarctic sea ice extent has been increasing, largely because of a change in wind patterns. Winds blow ice away from the coast, leading to more open water, which leads to more sea ice formation. Even though Antarctica is getting warmer, it's still much too cold to melt sea ice in most places, so climate warming isn't having a huge direct effect on sea ice.
However, the land ice in the Antarctic is almost certainly decreasing (exact measurements are quite hard), and the trend is definitely towards more ice loss. Ice shelves, although floating, are the outer extremes of this land ice.
Though it would take a huge temperature rise for that to happen -- enough that the other climatic effects would probably be as bad or worse than the sea level rise.
Greenland is not nearly so cold, so it's more likely that its ice shelf would melt, which would add about 7 meters (20 feet) to sea level.
The larger problem with melting sea ice, as I understand it, is that the reflectivity of water is much lower than that of ice, so less of the incoming energy from the sun is reflected, accelerating warming.
The antarctic is fundamentally different from the Arctic (it is the Arctic that is the canary in the coalmine for global warming). It is surrounded by >30 degrees of latitude of water, and the Coriolis effect ensures that winds blow without the interference of land around the globe between the roaring forties and screaming sixties. This insulates the antarctic and is the main reason it is colder than the Arctic - there is little heat transfer from warmer latitudes. In contrast, the Arctic is all about heat transfer and global warming simulations show it will warm much faster than the antarctic.
