Yes, it is. The government gives tax breaks to married couples, and pays for the courts to regulate the dissolution of marriages. That makes it their business.
Strawberry.
Beerina is, actually, on the right track. If you accept the notion that the legal status of marriage is predicated on tax and immigration law then marriage becomes just another government privilege and not a right. Why? Because the government, not the principals of the relationship, end up defining the relationship.
I find nothing in Article I, Sec. 8 of the US Constitution that enumerates the power of the Federal Government to intercede and arbitrarily define what a marriage is. Believe it or not, the Constitution is
not a "living and breathing document" subject to the whim of changing times, politics and opinions. If that were the case there would be no need for Article 5 or the 18 enumerated powers in Article 1, Sec.8. We could simply rename the document from "The Constitution" to "The Suggestion of the Church of What's Happenin' Now". Elect a new government every 2, 4 and 6 years and wait to see what your rights are by about April (Congress can act quickly when properly motivated). Your "guaranteed" rights would not be quite so guaranteed.
I do, on the other hand, find that the 9th Amendment instructs the Federal Government not to enact laws in such a manner as to deny the people of other non-enumerated rights. Though not a part of the Constitution, the Declaration of Independence states that we are "endowed by [our] Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness." That statement indicates that we have other unalienable rights in addition to life, liberty and the pursuit of happiness. The 9th Amendment, which is rarely called upon, clarifies that phraes in the Declaration. The 10th Amendment further supports the position. If the Constitution does not specifically enumerate a power to the Federal Government or deny it to the State government is it the sole power of the State or The People to decide. If the recent New York marriage law is correct in stating that marriage is a fundamental right then neither the Federal or State government has authority to deny or abridge the right of the people.
Does polygamous marriage create problems? Of course it does. As a strictly moral position I'm opposed to it. My moral position does not trump the Constitution. People make choices and have to live with the expected or even unexpected results. You want to contract for a polygamous marriage, go fo it.
All that I ask is that if it doesn't work out as planned please don't ask me to pony up and pay the cab fair to make it right. It's not my problem and it's not the government's problem. In general, asking the government to step in and solve a problem is similar to using an atomic bomb to rid your house of mice. Effective but somewhat messy - not to mention that it might cause a problem or two for your neighbors. But that's how government generally "solves" problems.