Okaay.
http://www.jag.navy.mil/organization/code_10_law_of_the_sea.htm
What they are politely referencing in part is that currently any nation can make a marine territory claim that prevents us from moving our ships where we want to, and it is hindering naval operations. We have no way to settle these today unless we have leverage over that nation, or unless we want to risk an international incident. The senators do nothing to solve this longstanding problem.
They see this as an issue of sovereignty. But we don't currently have sovereignty over the sea. And the effect of living without the treaty is that really small countries frustrate our navy and we cant' do a thing about it other than create international incidents left and right.
The last three administrations have supported this thing, and the Reagan Administration people are OK with the treaty after the 1994 changes. The Navy supports it because they are the ones that have to deal with the mess caused by the lack of a treaty.
I'm glad they think that bilateral negotiations with Russia have worked out. But with all due respect this is more reflective of what's going on:
http://byers.typepad.com/arctic/2012/02/toward-a-canada-russia-axis-in-the-arctic.html#more