While I was home for winter vacation I had the chance to read Newsweek's Our Mutual Joy (by Lisa Miller). While the article most likely mangles the Christian theology behind marriage badly, I cannot speak about that since I don't know Christian theology. I can speak to how it badly mangles Jewish theology. I am deliberately quoting passages from the article out of order, so that I can make an argument in a sensible order.
But as Segal says, if you believe that the Bible was written by men and not handed down in its leather bindings by God, then that verse was written by people for whom polygamy was the way of the world.
My first objection to Newsweek's article is that it assumes that ideas such as the documentary hypothesis (that the Torah was written by man) should define religious belief. Whether one accepts the documentary hypothesis or not, certainly the premise of the documentary hypothesis is in contradiction to the religious premise that the bible was authored by God. Thus, statements about the meaning of the text based on an argument that "the Bible was written by men" have no bearing on the religious truth of an argument based on the bible.
The Bible does condemn gay male sex in a handful of passages. Twice Leviticus refers to sex between men as "an abomination" (King James version), but these are throwaway lines in a peculiar text given over to codes for living in the ancient Jewish world, a text that devotes verse after verse to treatments for leprosy, cleanliness rituals for menstruating women and the correct way to sacrifice a goat—or a lamb or a turtle dove. Most of us no longer heed Leviticus on haircuts or blood sacrifices; our modern understanding of the world has surpassed its prescriptions. Why would we regard its condemnation of homosexuality with more seriousness than we regard its advice, which is far lengthier, on the best price to pay for a slave?
I imagine there may be some sense in noting that Christians have superceded and nullified parts of the Hebrew bible based on statements in the later Greek additions. Nevertheless, Jews do not accept the addition of "biblical" books hundreds of years after the end of the Hebrew bible, by heretics against the Judaism, and Jews have not eliminated these commandments. What of the fact that we're not concerned (today) about leprosy or how to sacrafice a goat?
The disease that is translated as leprosy (צרעת) is in fact something different (as many commentators go to great lengths to prove) and has not been seen in centuries. Our lack of concern with the treatment of the disease has only to do with the fact that we do not see it anymore, and does not indicate that any other commandment in the Torah is irrelevant.
Offerings can only be offered on the Temple in Jerusalem on the Temple mount. Because of our many sins, the Temple lies in ruins and Muslims control the Temple mount. Since the temple was first built by King Solomon, it is forbidden to make an offering on an altar anywher else, even when the Temple lies in ruins. However, Jews pray 3 times a day that the temple should be rebuilt and we will return to offering sacrifices. Our inability to do so now does not mean that any other part of the Torah is irrelevant.
Cleanliness rituals for mensturating women (niddah in Hebrew) are certainly still relevant and observed today. See here for instance. Most issues of purity aside from niddah are only relevant when we are concerned with the ability to go into the Temple, which as I have already mentioned is no longer standing, so their irrelevance today does not mean that any other part of the Torah is irrelevant.
Jews are also careful about the commandment on haircuts.
As we can see, commandments that are irrelevant today have a specific reason why they are irrelevant, and everything else we still follow.
(The fact that homosexual couples cannot procreate has also been raised as a biblical objection, for didn't God say, "Be fruitful and multiply"? But the Bible authors could never have imagined the brave new world of international adoption and assisted reproductive technology—and besides, heterosexuals who are infertile or past the age of reproducing get married all the time.)
Though there are a lot of things that are good about assisted reproductive technology, some of the things such as in-vitro fertilization with a sperm donor are actually extremely probalematic in terms of the Torah prohibition of adultery. Just because a technology seems like a good thing, and has effects that we consider to be "good ends", this does not mean that it is necessarily moral.
In the Old Testament, the concept of family is fundamental, but examples of what social conservatives would call "the traditional family" are scarcely to be found. Marriage was critical to the passing along of tradition and history, as well as to maintaining the Jews' precious and fragile monotheism. But as the Barnard University Bible scholar Alan Segal puts it, the arrangement was between "one man and as many women as he could pay for." Social conservatives point to Adam and Eve as evidence for their one man, one woman argument—in particular, this verse from Genesis: "Therefore shall a man leave his mother and father, and shall cleave unto his wife, and they shall be one flesh."
Polygamy was eliminated in the Christian world in the sixth century. In the tenth century, Rabbeinu Gershom banned it amongst European Jewry, largely so that it would not appear that the Jews were less moral than their neighbors. It remained permitted in other locales (such as Yemen) until as recently as the founding of the state of Israel. Given the fact that homosexuality is banned by the Bible, and polygamy by Rabbis, this actually makes homosexuality worse than polygamy. It is a modern interpretation of marriage (not necessarily religiously motivated) that drives the view that polygamy is worse. In fact, it may only be the modern trend toward the permissability of homosexuality that drives this trend.
In conclusion, Lisa Miller's article is not a religious attempt to justify gay marriage, nor even an attempt to justify gay marriage from the bible. She mistakenly concludes that certain modern sensibilities are more "religious" than the statements of religious teachers over the ages, thereby misunderstanding what religion is. Her attempts to support gay marriage from the bible are merely attempts to say "we should dismiss this too, just as we dismissed other parts of the bible becuase of our modern sensibilities." Don't be fooled.
A distortion that the article did not make (thankfully) but others frequently make is an attempt to creatively interpret the verse in Leviticus (18:22, "You shall not lie with a man as one lies with a woman." These creative interpretations are actually rather irrelevant to Judaism. Though the scope of the actual prohibition in these verses is not irrelevant, there are other sources to consider too. The written Torah is at best a very cryptic primary source for Jewish practice. The ways that we learn Jewish practice from it rely so much on hints in the Hebrew text that the text itself is practically indecipherable. Any version of Judaism today that legitimately considers itself Jewish relies on other sources such as the Talmud, Midrash, and Zohar as primary sources as well, since they carry the correct understanding of the Torah text based on the rules that we have for interpreting these hints. The Talmud (in tractate Chullin 92b) is clear that it is forbidden (even among non-Jews) to write a marraige contract between two males, and the Zohar and Midrash go into great length to explain that writing marriage contracts between two males, and between men and animals was the reason why God brought the flood upon the world. Though the verse in Leviticus does seem rather narrow, we have other primary sources which are not so narrow.
Regarding the issue of what commandments are intended for Jews only and what commandments are intended for Jews and non-Jews, see this article about the Noachide laws
I should note that the Wikipedia article on Midrash discusses the idea of "Contemporary Midrash". Only the works listed as "Classical Compilations" on Wikipedia are considered primary sources in Judaism. The things labeled "contemporary midrash" are a misuse of the word "midrash" and bear on relation to Judaism's primary sources.
There is argument about the authenticity of the Zohar as a whole, but by and large it is accepted today as authoritative.