Hawaii was long considered the state most likely to approve same-sex marriages, but even in the Aloha State there's limited popular support for the idea, where voters passed a amendment banning the practice in 1998 by a 2-to-1 margin. 

Most states have banned same-sex marriages, and Congress has passed the Defense of Marriage Act.  The Act gave states the right to ignore same-sex unions licensed elsewhere, while at the same time denying federal recognition of homosexual unions.