Senator Charles ("Chuck") Schumer of New York faces a particularly tough choice: back Obama's Iran deal and anger many of his New York Jewish constituents, or oppose the deal and anger Obama and much of the Democratic Party leadership.
My prediction: Schumer will cave to Obama and cling to his own long-nourished hopes of one day succeeding Harry Reid. Or he will take the weaselly option mentioned
here, voting to override Obama's veto of a Congressional bill to continue sanctions but being careful to not bring along enough people with him to make an override stick. Schumer, as the probable heir apparent to Reid's position, seems to have quite a bit of influence over his fellow Democratic senators who are likewise hesitating, and therefore his vote is considered a sort of bellweather or linchpin.
As for the vote itself,
here's a good discussion of the "is the Iran deal a treaty or not?" question, from back in March:
There is no currently no suit on the issue [of its being a treaty] being discussed on Capitol Hill, and it's far from clear that Republicans would be standing on firm legal ground with such a challenge. The debate, rumbling for decades, has yet to be definitively resolved in case law.