For most of Western history, marriage was a private contract between two families. Until the 16th-century, Christian churches accepted the validity of a marriage on the basis of a couple’s declarations. If two people claimed that they had exchanged marital vows—even without witnesses—the Catholic Church accepted that they were validly married.
Marriage licenses were introduced in the 14th century, to allow the usual notice period under banns to be waived, on payment of a fee and accompanied by a sworn declaration, that there was no canonical impediment to the marriage. Licenses were usually granted by an archbishop, bishop or archdeacon.
In the United States, until the mid-19th century, common-law marriages were recognized as valid, but thereafter some states began to invalidate common-law marriages. Common-law marriages, if recognized, are valid, notwithstanding the absence of a marriage license. The requirement for a marriage license was used as a mechanism to prohibit whites from marrying blacks, mulattos, Japanese, Chinese, Native Americans, Mongolians, Malays or Filipinos. By the 1920s, 38 states used the mechanism.
Some groups believe that the requirement to obtain a marriage license is unnecessary and/or immoral. The Libertarian Party, for instance, believes that all marriages should be civil, not requiring sanction from the state.[8][9] Libertarians argue that marriage is a right, and that by allowing the state to exercise control over marriage, it is implied that we merely have privilege, not the right, to marry. As an example, those born in the US receive a birth certificate, not a birth license.[10] Some Christian groups also argue that a marriage is a contract between a man and a woman presided over by the Christian God, so no authorization from the state is required. In some US states, the state is cited as a party in the marriage contract[11] which is seen by some as an infringement
http://en.wikipedia.org/wiki/Marriage_licence
Does this mean that the government must recognize polygamous unions that are recognized internationally?
Your argument does not nullify the fact that marriage has been recongized LEGALLY for thousands of years, whoever does the official marriage ceremony.