Kim Davis was elected into her current occupation, and is being paid to do what her job requires of her to do. If at any time she felt that whatever her job required caused her a conflict of conscience with her Christian faith, she has the right to ask for accommodation if it can be given. I understand in her job no accommodation can be given, so therefore she has one option open in regards to standing on her Christian faith: She can resign.
Now, let’s look at this from another angle and see the proper route she should have taken in defense of her actions.
When Kim Davis was elected to her office, my understanding from many news sources is that she took an oath to defend her state’s constitution and all other appropriate laws. This does not include any judge’s opinions, because those are not laws; only legislatures can make laws, while judges can only issue opinions as to whether a law is proper; a problem with Americans is that they too often accept a court decision as a law and it isn’t!
Kim Davis elected instead to make an issue of her faith, while at the same time violating Romans 13 by refusing to obey the governor and judges rather than resigning, and then everyone is misrepresenting the case by claiming she is being jailed for her Christian beliefs.