If you have a religious conservative in your life who thinks that Kim Davis is a hero, ask him if he understands the concept 'pluralism'. Ask him if he understands that the whole idea of religious freedom is to allow everybody to practice and believe what he wants without government interference.
Government is a civic institution, and its scope of responsibility is exclusively about civic issues. The government has no interest in marriage except that it is a civil contract between two or more parties. It should allow the Mormons to be polygamists, too, if it's just a matter of setting up the contracts between adults. It should make no moral judgments. It can't in a pluralistic society where there are so many different kinds of beliefs. It has to remain neutral and non-judgmental. It treats within its sphere all religions and beliefs and lifestyles equally (so long as there is no harm), and in doing so protects Kim Davis from some future government preventing her from practicing or believing as she wants.
So let's take her at her word that she truly believes that it's against her conscience to issue these licenses to gay couples. What are her options? The first is resignation. Issuing these licenses will be a normal part of her job going forward, and she cannot in good conscience perform the job the voters elected her to do.
Another option would be civil disobedience, to remain in the job while refusing to issue the licenses in the expectation that she will be impeached. She could then use the impeachment proceedings to explain why she feels the law is unjust. Then she should let it will play out in the political sphere as it will with constitutional amendments if there is the popular and political will to effect them.
Either way, she cannot function in that position unless she agrees to follow the law by issuing the licenses. Ultimately the test of Davis's convictions is not how much jail time she does, but whether she stays in the job. She cannot be taken seriously if she remains in it. If she's sincere in her convictions, we should be hearing either a resignation announcement or that she will be going through an impeachment process. Any kind of compromise to stay on the job will prove that she isn't morally serious.