The state of Kentucky has an obligation, now that their law has been declared unconstitutional, to pass laws clarifying a number of issues related to same sex marriages. One of those laws should protect and accomidate people of faith. Many states have done that. More should.
But the case of Kim Davis does involve a constitution. The constitution of Kentucky, which 75% of Kentucky voters opted to amend in a referendum from 2004. In that amendment, same-sex marriage, or any “legal status identical or substantially similar to that of marriage” was specifically outlawed. You might think that terrible, you might think it unjust, you might think it tyrannical, but that is the law in Kentucky. To throw someone into a Kentucky jail for upholding it, is nothing short of an act of war by the federal government against the state of Kentucky.