In 1972 the U.S. Supreme Court dismissed an appeal from a ruling from the Minnesota Supreme Court upholding the denial of a marriage license to two men.
http://en.wikipedia.org/wiki/Baker_v._Nelson
If Hubert Humphrey wins the 1968 presidential election and appoints social liberals to the Supreme Court it might just be possible to get the Supreme Court to actually hear that case and have a majority vote to guarantee same sex marriage as a constitutionally protected right. Justices William Brennan and Thurgood Marshall would just three years later in OTL support overturning a Virginia anti-sodomy law in Doe v Commonwealth's Attorney, so it's possible they would both be open to legalizing same sex marriage. Justices William Douglas and Abe Fortas (if he's still on the court) might likewise be sympathetic. Thus there are already potentially 4 gettable votes at the Supreme Court for same sex marriage. President Humphrey will get at least 3 appointments (replacing Warren, Black, and Harlan), so if just one of his new appointments is willing to vote for same sex marriage than it could be federally legalized sometime in 1973.
Now that said such a ruling would probably ultimately prove disastrous for the cause of same sex marriage in the United States since the ruling would probably be quickly overturned by a constitutional amendment defining marriage as between one man and one woman, and once a ban on same sex marriage was enshrined in the Constitution it would be very difficult to undo. However, the United States would still technically have been the first nation to legalize same sex marriage at the federal level (even if that decision did subsequently get reversed.)
