Menendez, Schumer, Cardin and maybe even some other Democratic senators (Booker?) will eventually vote against it, but they won't get to 13, which means that Obama's veto won't be overridden.
Whatever the chances of it being overriden in the Senate, it's effectively 0% in the House, so the Senate might as well just stay home. I assume the next POTUS can just negate the whole thing, since it is not a treaty, and this weird process was just a meaningless bone Obama tossed out to get something else done, I forget what. That question come to think of it, should be brought up in the debates.