I sort of doubt it, primarily because fighting a case up to the Supreme Court generally takes an enormous amount of very expensive legal work, and there are probably not enough people invested in the issue to do it - but you never know.

I personally feel it ought to be allowed, on the simple basis that people should be treated as free agents who can enter into whatever connubial relations they choose. It's disappointing to see many advocates of same-sex marriage apparently attempt to pull up the ladder behind themselves by offering obviously specious arguments against such arrangements; while this is an understandable reaction to conservative 'gotcha!' arguments against same-sex marriage, it is needlessly hurtful to people who are in voluntary poly arrangements. I'm not one of those people, but I have known quite a few folks who live in polyamorous relationships and those arrangements have been no more or less problematic than monogamous pairings, so I don't feel they are constitutively deficient.

One popular objection is to point to the low status of women in societies where polygyny is widespread, eg Saudi Arabia. However, it's far from obvious what sequence of events led to current conditions; polygyny may have originated as a rational response to intense tribal warfare in a harsh environment and correspondingly low life expectancy for male combatants. It does not follow that availability of legal plygamy will necessarily or even probably lead to the same outcomes. While it's anecdotal, my personal acquaintance with poly households in the UK and US has been that more of them were steered by the preferences of women members than men, but that's purely anecdotal.

The historical status of women in polygyny should absolutely be taken into account and studied carefully, but I think there's a chicken-and-egg problem insofar as abusive/exploitative arrangements almost invariably present with religiously-grounded arguments about male superiority in male-identified monotheistic religious contexts. It seems to me that if you begin from the premise that 'there's only one source of Cosmic authority, he's a guy, and he only talks to guys' then women's status is going to be massively discounted in such an environment, regardless of how many parties there can be to a marriage. In short, I doubt it was the case that everyone was living in egalitarian bliss until someone invented polygamy and caused everything to go downhill. On the other hand, this is a genuinely-felt concern, since sex discrimination is still rampant in many parts of the US notwithstanding the nominally egalitarian legal framework, so I don't blame anyone for predicting that legal polygamy would be exploited for the worst possible reasons by some people - but if the possibility of negative outcomes were the only factor, we'd make it much harder for people to get married or have children in the first place, given the frequency of numerous awful outcomes under plain old monogamy.

Imbalance in sex ratios is beyond the scope of a HN comment, but there is some interesting research suggesting that different patterns are strongly correlated with different economic relations and environmental conditions, and also pointing out that polyandry is historically somewhat more widespread than most people imagine: http://www.theatlantic.com/health/archive/2013/02/when-takin...

The NYTimes article mentions the 'marriage market' approach of some thinkers (notably Judge Richard Posner, who is well-qualified to make such analyses), but all of those arguments seem predicated on the implicit assumption that women would flock to being collected by wealthy men and thus leave other men with nobody to marry. Certainly some people do marry for money (quite a lot of them in fact) but this seems me like an uncritical assumption of rational-choice economic theory as the ground of truth, whereas work by behavioral economists strongly suggests otherwise.

One other argument raised against polygamy is the complexity of inheritance, divorce and so on, which is invoked as an inevitable Gordian knot that would cause the court system to grind to a halt. However, none of these people seem to have considered that we have had commercial arrangements in the form of limited partnerships for centuries, and as a result have a well-established body of business law on how those should work, how responsibilities and benefits should be decided, how they should be dissolved or individual members added or removed, what should happen if a partner dies or goes to prison and so on and so on. Most people conceive of marriage as a bilateral contract, but multilateral partnerships are actually common and while they give rise to complex problems of their own I don't think there's anything inherently intractable about such a setup.

I really wouldn't expect impending legal challenges to go anywhere and very much doubt that we'll see legal polygamy in the US within the next couple of decades. But as I've outlined above, I don't believe there's anything sacred about the pair bond. While pair relationships are a simple fact of reproductive biology- as in I've never heard of anyone inheriting from 3 sets of DNA - it's well established in law that reproductive biology is not and can not be the yardstick by which social relations must be measured. I hope people will keep an open mind and consider the possibility that people who are willing to invest the extra work involved in a polygamous relationship should have the opportunity to do so.