Can she be jailed for contempt?

Good article in the Atlantic on why Davis' legal argument won't hold water in the courts should she continue to pursue this.....

.......Let’s understand who’s in court right now. On one side are five same-sex couples who want their licenses in their own county; on the other is Davis, who wants to be free to refuse them and send them elsewhere. There’s no middle ground here—a court could hold for the plaintiffs and order Davis to do her job, or it could hold for Davis and tell the couples to go elsewhere. Those are the only two options.

But as presented by her lawyers, the real fight is between Davis and Steve Beshear, the governor of Kentucky. Immediately after the Court’s decision in Obergefell, Beshear issued an order to the 120 county clerks in Kentucky ordering them to issue same-sex marriage licenses; he also ordered the state’s Department for Libraries and Archives to prepare a new license form using gender-neutral language. Davis’s application for a stay, in effect, asked the Supreme Court to tell the governor that he has misused his authority under Kentucky law, and then order the Kentucky state government to pass new statutes and issue new regulations.

It’s those actions, not the request by the local parties, that Davis argues violate her religious freedom. Not only that, she argues, Beshear went beyond his state-law authority and “effectively commandeered full control of Kentucky marriage law and policy.” Davis wrote a letter to Beshear asking him to call a special session of the legislature, but he didn’t answer. Beshear’s order “imposes a substantial burden” on her religious beliefs; in fact, “by way of Gov. Beshear’s SSM mandate, Davis is being threatened by loss of job, civil liability, punitive damages, sanctions, and private lawsuits.” He is “imposing a direct and severe pressure on Davis by the SSM Mandate.” And thus the governor “must demonstrate by clear and convincing evidence” that his order does not violate the First Amendment and the Religious Freedom Restoration Act.

But Steve Beshear is not before the court right now. On August 4, more than a month after the original case was brought, Davis filed a “third-party complaint” against Beshear, seeking to bring him into the case. That complaint argues that Beshear “has exposed Davis to the Plaintiffs’ underlying lawsuit.” The case could be resolved easily, the application argues, if the governor and the legislature would just change the state statute that requires a county clerk to issue same-sex marriage licenses.

Mark Joseph Stern of Slate recently wrote criticizing her lawyers, the religious-legal charity Liberty Counsel. He called the emergency stay application “an angry, rambling application to the Supreme Court that is little more than an anti-Obergefell rant dressed up as a legal document.”

I’m not sure I agree with that. I do think, as Stern says, that Liberty Counsel made a grievous error in advising Davis to defy the court’s order. And God knows the firm is easy to mock. (Its website features a statement by Davis that “to issue a marriage license which conflicts with God’s definition of marriage, with my name affixed to the certificate, would violate my conscience”—and beneath it, a request for a $25 donation in exchange for a book in which “two nationally-acclaimed real estate entrepreneurs share biblical principles to revolutionize your work and family life, and give you the courage to stand up for what is right.”) But the stay application did a reasonable job of stringing together the Court’s loose rhetoric in Hobby Lobby to support the implausible contention that government officials have a religious right to refuse to serve people they disapprove of.

The real flaw in the stay application is less the substance of its argument, than the fact that the argument is aimed at Beshear. In effect, Davis and her lawyers asked the Court of Appeals, and the Supreme Court, to wade into an ugly political fight about Kentucky law. The Supreme Court may eventually create some exemptions for marriage objectors; that’s not beyond the realm of possibility. But the likelihood that it will tell Beshear and the Kentucky General Assembly what orders and laws they should write is vanishingly small.

If I actually wanted to win a stay of the injunction, I wouldn’t have made those arguments. If I were a clerk or a Justice—however sympathetic to religious freedom I might be—I wouldn’t touch this dog. A good case will come along, with a petitioner who obeys courts and lawyers who know what they’re doing.

If a spiritual conflict prevents one from doing her job, the honorable thing to do is resign.

It is not for her to decide if others may marry.

Hope she reflects upon that while in jail.

Is someone else issuing licenses?

Yes.  Five of the six deputy clerks are doing it.  One is not.  The one that is not is this lady's son. I guess she got him the job sometime in the past.
 

In these personal belief vx. public responsibility conflicts I believe Martin Luther got it pretty much dead right:  A clear distinction must be made between the person (and whatever Christian views they hold) and the public office, which may very well require the Christian to act in a way that s/he might not (and/or may not) do in private life.

His favorite example was the magistrate, who has the power to sentence capital punishment (16th century Saxony jurisprudence).  Personally the magistrate has no such power and might be totally opposed to the death penalty BUT BECAUSE OF HIS OFFICE hs is compelled to pass sentence.