We’ve done this debate recently around here.
SSM hinges on the Equal Protection clause of the US Constitution. Currently homosexual people, as a group, do not enjoy “protected” status under EP jurisprudence. However, when you look at it, they almost certainly should be given the tests the courts have used to decide if a group requires protection. You can argue it of course. Justice Scalia thinks they fail the test because they are politically powerful as a group (which is one of several criteria that all have to be met).
Polygamists can never make the case that as a group they require “protected” status anymore than skate boarders can claim protected status. As such they would get nowhere in the courts with this argument where SSM couples certainly can make a case for themselves. This leaves the door wide open to the government to continue to ban polygamy.
Additionally, even if you want to suppose polygamists deserve EP protection same as SS-couples, the government has an out when they have a “compelling interest” at stake. This goes to the harm that polygamy can bring about which is far more than a, “We think it is icky” argument.
Polygamy is fraught with problems. As it has been and is practiced it is distinctly not equitable. One would assume that in the US we’d allow it to work both ways (one woman, multiple men/one man, multiple women or even multiple women/multiple men). The problems become hugely difficult mainly when someone wants to leave the relationship.
Lets say woman #2 want to divorce. Can she force the sale of the house to get her share of the equity out? How much equity does she have? If there are three wives and one man does she get 1/4? That would leave the whole rest of the family and kids without a home. What if she came along 5 years after wife #1. Does that diminish her equity in the house? What about the kids? If the man wants to retain custody can he now argue wife #2 would be taking the kids away from their brothers and sisters? Can wives 1, 3 & 4 team up to say what a bad mom #2 is? Would you trust their testimony? Does spousal privilege obtain to everyone in the house or just between the woman and the man?
The list goes on. It’d be a mess. What if you had one woman and multiple husbands and the woman dies (accident, sickness, whatever). Do the husbands now have to do paternity tests to see which kid is theirs and then they scatter? Do they have to stay together for the kids? If one wants to go but the others want to stay can they override the one? If they stay together do they have to jointly find a single woman they all want to marry or can they marry individually? If they can mary individually and they are still living together do the other men have a veto on the marriage?
The possible troubles boggle the mind.
SSM requires no change in the law. So no, SSM does not come close to opening the door for plural marriages.