Of course the entire northern ice cap could melt and there would be no effect on sea levels. Floating ice displaces it's own mass of liquid water. Thus the melted ice would fit in the volume of water it was pushing out of the way previously. The amount of snow/ice being supported by land (Northern Canada and Greenland) is relatively small.
 

One wonders how the human migration across the (now) Bering Sea was accomplished if ice/snow accumulation cannot shrink the extent of oceans.

Few studies I am aware of predict no change for sea levels given glacial melting.

But then, I live in Illinois.
 

From Wikipedia (and no, I didn't make this entry myself).
Ice shelves float on the surface of the sea and, if they melt, to first order they do not change sea level. Likewise, the melting of the northern polar ice cap which is composed of floating pack ice would not significantly contribute to rising sea levels. Because they are fresh, however, their melting would cause a very small increase in sea levels, so small that it is generally neglected. It can however be argued that if ice shelves melt it is a precursor to the melting of ice sheets on Greenland and Antarctica[citation needed].
http://en.wikipedia.org/wiki/Sea_level_rise#Glaciers_and_ice_caps

No doubt a disappearing Northern Ice Cover would not be a good sign... It just wouldn't have much of a first order effect. I wonder how much difference it would make in absorbed radiation from the sun, as the suns rays are at such a low angle anyway.