Most of the Arctic ice is not resting on a landmass, so if it melts, the water level stays the same. Just like an ice cube melting in your drink does not overflow your glass.
Only Greenland has any land underneath, if I’m not mistaken. Massive melting of it’s ice shelf would affect world sea levels.
Antarctica, on the other hand, definitely has land underneath the ice shelf. Whatever melts from there is added to the current level.
Dropping massive amounts of ice into the oceans (as large slabs of ice break off and fall into the water) also affects water currents and wind patterns. So even if the water level does not change enough to cause massive flooding, more severe weather (such as tropical storms and hurricanes) might make life “interesting” for some regions.
That said, the whole “Global Warming” thing is based on hard-to-test science. There is a lot of suppositions and assumptions being “accepted” with little concrete evidence. A lot of data comes from computer models. The problem is to determine whether those models are accurate for real world predictions.
It appears that having ice at both poles has been a relatively rare event in the Earth’s history. Whether we’re having an impact, and whether it is significant is a lot more debatable than most media reports would have you believe.
The consensus among Soviet scientists is pretty much the opposite from the western ones: they don’t believe that Global Warming is caused by man, but simply a natural cycle of the Earth.