So What If All the Icecaps Melt?

I was sitting here watching the ice melt in my cup, remembering something from physics, and thought I'd push some buttons. The physical principle is this: the amount of water displaced by a mass is equal to the volume of the mass. In other words, it doesn't matter the form of the matter, it will take up the same amount of space.

Back to my cup. Most of us have had a nice, large cup of ice water outside on a hot day. Yet, we've never experienced an overflow when the ice melts. This is because of the principle stated above. And if the principle holds true for my cup of ice water than it should hold true for icecaps in the ocean, regardless of size.

I have thought of this occasionally but have never been able to find a satisfactory answer. Is there something special about icecaps that their melting would cause sea levels to rise? Is something different altogether at play?Links, please.