I just wanted to add that the US Supreme Court did have a similar case in front of it back in the 60's.

Here's the heading from findlaw.com

U.S. Supreme Court
LOVING v. VIRGINIA, 388 U.S. 1 (1967)
388 U.S. 1

LOVING ET UX. v. VIRGINIA.
APPEAL FROM THE SUPREME COURT OF APPEALS OF VIRGINIA.
No. 395.
Argued April 10, 1967.
Decided June 12, 1967.

Virginia's statutory scheme to prevent marriages between persons solely on the basis of racial classifications held to violate the Equal Protection and Due Process Clauses of the Fourteenth Amendment. Pp. 4-12.

I believe a very similar argument could be made about any laws barring same-sex marriage in the U.S.