Why wouldn't they support the right of gays to marry? Why wouldn't they support the legalization of marijuana? Why wouldn't they support a woman's right to an abortion? The Republican Party's problem isn't their ability to message; their problem is their message itself.
Any public policy or law that places a badge of inferiority on certain "less desirable" personal relationships should be struck down. Marriage as a form of expression is a civil, if not an inherent, right.