Several couples are expected to show up at the Rowan County office after 5 out of 6 deputy clerks told the judge they will distribute the certificates, reports CBS News correspondent Dean Reynolds.
Same-sex marriage advocates cheered Wednesday after the judge ordered Davis to jail.
The decision dealt a heavy blow to those who showed up to support the Rowan County clerk.
"I came here because of my children. I wanted them to see this moment in history where this courageous Christian woman is willing to defy tyranny," one woman said.
Inside the courthouse, the Apostolic Christian broke down as she talked about her faith, and said she was unable to issue marriage licenses to same-sex couples insisting "my conscience will not allow me."
"Marriage," she told the court, "is a union between one man and one woman. God's moral law conflicts with my job duties."
But the judge said her "good faith belief is not a viable defense." He held her in contempt and ordered to keep her behind bars until she ended her defiance.
The judge then gave Davis a second chance, offering to release her if she promised not to interfere with employees who had agreed to issue the certificates, but Davis rejected the deal.
"Ms. Davis is in an unfortunate situation of her own creation. She is not above the law...She is not a martyr," the plaintiffs' attorney Laura Landenwich said.
Until she complies, the judge said Davis will remain locked up.
"She told the judge, 'Don't matter what you say. I'm not settling,"' her husband, Joe, said.
One couple, April Miller and Karen Roberts, plan to apply for a marriage license in Rowan County for a fourth time.
"As a couple, it will be a very important day in our lives," April said.
Along with Davis, her son is the only other holdout in the clerk's office. But the judge said he won't face any fine or jail time.