Possibly. Influence is difficult to measure, and the decision ultimately rested in the mind and heart of each state senator... but possibly. Zeek reprints an open letter from Rabbi Steven Greenberg, the first openly gay Orthodox rabbi, to Sen. Steven Saland of Poughkeepsie, one of the two crucial Republican swing votes. In the letter, Rabbi Greenberg appeals to the memory of Saland's rabbinic ancestor, Rabbi Shmuel Salant -- a tactic shared by Agudath Israel in their own appeal to the senator, from the opposing side.
Whether Rabbi Greenberg and the Agudah had any impact or not, Saland voted for the measure in the end, putting the legislative question to rest in the state of New York. But within Orthodox Judaism, the question of how to relate to the modern world's ever-solidifying acceptance of homosexuality will continue for many years to come. Rabbi Greenberg, of course, is a significant voice in this internal debate, as are other gay Orthodox Jews, whose personal experiences make this issue impossible to ignore.
Yet, for all the consternation that this issue understandably causes in Orthodoxy when it comes to questions of halakhah, ritual, and other internal matters, it is somewhat baffling that Orthodox Jews should feel the need to maintain a correspondence between secular and religious definitions of marriage. As Rabbi Michael Broyde and Rabbi Shlomo Brody point out in the context of an article articulating a clear and strict opposition to homosexual sex,
Politics makes strange bedfellows, especially in multicultural democratic societies like America. The pragmatic decision to support equal rights for gays in the political realm is not inconsistent with our view that the underlining activity violates Jewish (and Noachide) law. We support religious freedom for all, even as we are aware that some might use this freedom to violate Jewish or Noachide law. Similarly, it is wise to support workplace policies of non-discrimination based on sexual orientation, just as we support such non-discrimination based on religion, even though these laws equally protect, for example, pagans. Discrimination based on lifestyle choices may threaten our own liberties, including freedom of religious expression...
Rabbis Broyde and Brody go on to specify that both political opposition to and political support for same-sex legal marriage are within the realm of reasonable Orthodox choice:
If one believes a civil prohibition of same-sex marriage does not threaten our rights in the long term, then joining a political alliance opposing such, based on shared values or interests, seems reasonable. If, however, one views such a campaign as an infringement of civil liberties, or a potentially bad precedent that might endanger our interests in other areas of civil life, then one should not feel compelled to combat gay marriage.
If this is not a ringing endorsement of civil marriage equality, neither is it the stance of clear opposition taken by the Orthodox Union.
The Orthodox argument in favor of maximum liberty is not a recent invention; as the blog Failed Messiah notes, Rabbi Moshe Feinstein was essentially anti-abortion (except to save the life of the mother), and yet also essentially pro-choice. "In Rabbi Feinstein's view, the decision to abort was a decision that should be made by the woman and her rabbi, not by Congress."
Ultimately, as homosexuality becomes increasingly normalized in the broader world, Orthodoxy's internal and external stances on this issue will be increasingly tested and challenged.