So she has been refusing to issue ANY marriage licenses since June, her defense being that issuing a marriage license with her name on it as county clerk is an endorsement of the marriage. Courts have disagreed with her, citing that she took an oath that she is supposed to uphold as elected county clerk. It's not that she's refusing to do this herself, it's that she is refusing to let ANYONE in her office issue a marriage license.
Her legal options have been exhausted since the Supreme Court refused to hear the appeal of the court order to issue marriage licenses. She has now been ordered to jail until she decides to comply, as she is currently in contempt of court.
My personal thought is that she is fully within her right to her beliefs, but if those beliefs make it such that she cannot uphold the oath she has taken, she needs to step down. Instead of stepping down (or even stepping aside), she has flat out refused to follow court orders. What I find interesting is that her attorneys have insisted that any court ruling in favor of gay marriage is inherently illegitimate because it violates religious precepts.