Davis is stuck in her position because the gay law was passed while she was in office. She does not want to loose her job. Would anyone? And she claims that she cannot violate her conscience. She is stuck.
There was no gay law passed, the supreme court ruled on laws that were attempting to ban same sex marriage, striking them down and ruling they were unconstitutional.
Davis is stuck only because she can only think in simplistic, black and white terms and wrongly feels that her name on the marriage licence would mean she is approving of the marriage, when all that means is that she has certified the marriage is legal. Frankly, I don't think she is the sharpest pencil in the drawer, and she is more motivated by hate than belief, but whatever her reason, she is wrong.
Now that she is in jail she is attempting to reach some kind of compromise that will allow her to take her name off of the licenses and keep her job. I personally don't want to see her lose her job, but she has to learn that you can't flaunt the law and justify it by claiming it's because of your religious beliefs. Imagine the chaos that would ensue if that were allowed. Other people in other backwards counties are probably watching this to see what happens. Hopefully it will all get resolved and people will figure out they can't discriminate against gay people just like they learned they couldn't discriminate against women or people of color.
I agree this is likely a transition issue, hopefully it will get resolved and we can all go back to making fun of Donald Trump.