That is a multi layered question, even if you did not realize it.
The first thing is to distinguish the different types of marriage. If you asked couples if they would consider their marriage over if the government's of the US no longer legally recognized their marriage and all legal benefits were gone, most would tell you that they would still be married. So most people consider marriage as something beyond the legal paperwork. In that sense, there are hundreds to thousands of poly marriages across the country currently, and I a man currently in one. I have a husband and two wives.
I am guess that the overall intent was asking about the legal recognition and benefits of poly marriage. There are many in the country who would like to see it come about, most actually. But the biggest dividing line among us deals with whether or not we should pursue it directly currently, or go slowly, making changes to the law to make the addition easier. Unlike adding in same sex marriage, or even theoretically incest marriage, where all you are doing is removing any restrictions to the two person marriage model, the dynamics of a poly marriage would require a lot more thought and planning.
For me personally I am satisfied to wait. That only laws I want to see struck down right now are ones that would try to prevent us living as we wish. For example, out west somewhere, I think Utah, there was a law that basically forced common law marriage on people living together whether there was any legal paperwork to begin with or not. They would apply it to any they felt were living as if married, even if they didn't have the paperwork and then charge them with bigamy, or holding multiple legal marriage statuses. It was determined unconstitutional and entrapment, because the individuals were not seeking that legal status, and the courts said that such a status could not be forced upon such groupings with the intent to charge them. I'll see if I can find the story later.