There is a legal distinction between policy making duties and ministerial duties. The latter applies to contexts where the act or function is prescribed and involves following instructions to try to achieve uniformity and consistency of outcome and minimize discretion. The function of issuing marriage licenses is ministerial.
A court clerk must verify that a couple applying for a marriage license meets the requisite legal qualifications. If the legal qualifications to be married are met then the court clerk has no discretion to deny the marriage license. Conversely, if the legal qualifications to be married are not met then the court clerk has no discretion to issue the marriage license. Whether the government bureaucrat is an elected official or not makes no difference, a ministerial duty is not discretionary. Under Kentucky law, it is a class A misdemeanor for a government employee to refuse to carry out their ministerial duty.
Kim Davis has three honorable choices, and they are all bad. She can carry out her ministerial duty against her will, resign, or spend the remainder of her days as the elected court clerk on an extended leave of absence from her job under court order (possibly confined to her residence or jail). While she is absent from work, one of her deputies will issue the marriage licenses, possibly without the court clerk's signature. The county attorney, the governor, and the state attorney general have publicly asserted that the marriage licenses issued without her signature are valid. Kim Davis is litigating on behalf of her claim that she has discretion to refuse to authorize the issuance of licenses to legally qualified couples and licenses issued without her authorization are invalid. This is a sweeping claim with negative implications for the rule of law and thus will be difficult for judges to accept.
Her attempts to have the licenses declared invalid could result in a court decision requiring her signature to appear on the licenses. Maybe that is her real goal because with her signature on the licenses she can then try to make a freedom of expression violation claim. But a free expression claim would still be weak because her signature technically communicates only her judgement that the couple qualifies for the license under the law, it does not communicate that she personally endorses the marriages. Her claim that by authorizing the licenses while serving as court clerk she would be personally condoning same gender marriage, regardless of whether her signature appears on the license, is a dubious claim. Unfortunately, some legal precedents are excessively accommodating of such religious belief burden claims, thus encouraging them. But there is no room for judges to agree with Kim Davis without contradicting the Supreme Court decision mandating same gender marriage, so even the bad precedents will not help her case.
In my opinion, it would be better for the SCOTUS to impose an enforcement delay when they file controversial decisions like this that extend civic equality to disliked minorities. The length of the enforcement delay can be set to the length of time it typically takes an employed person to find alternative employment. Most government employees tasked with implementing the revised law will comply immediately. Those that refuse would have time to look for other employment before being confronted with the bad choices confronting Kim Davis. Misguided bigots, such as Kim Davis, are often otherwise law abiding citizens who need employment to pay their expenses. Government employees who continue to refuse to carry out their ministerial duties or resign after the enforcement delay expires would then find themselves coerced by the state into absenting themselves from their government employment. This strikes a balance between a short term protection of the civil right to employment opportunity for those government employees tasked with implementing the revised law on the one hand and the need to promptly revise the law to extend civic equality to those who have been unjustly denied civic equality for far too long on the other hand.
An enforcement delay could have postponed the day of reckoning until after the next Kentucky legislature session begins. The Kentucky legislature could revise the law to allow a court clerk deputy to authorize licenses and place their own signature on the license. Kim Davis has indicated that she would not stand in the way of granting licenses if they were authorized and signed by someone else.
People must be qualified for their employment, just like people must be qualified to obtain a marriage license. Whenever someone's beliefs disqualifies them from their current employment they become responsible for finding alternative employment. Freedom of expression and belief is not synonymous with freedom from being burdened by any negative consequences that result from following our beliefs. Nevertheless, government arguably does have some responsibility to give government employees an opportunity to find alternative employment before forcing them out when they become disqualified from their current employment due to a conflict with their beliefs as a result of a change in the law that they are tasked with implementing.