Although America is not a theocracy, Christianity is still culturally dominant, and, this time of year, especially, culturally prominent, so the question is worth exploring: Is it sacrilegious for the United States Senate to work during the Christmas holidays?
Theologians seek to understand ethical and religious questions by looking first at holy scriptures, then at the Christian tradition and shared experience. In many cases this time of year (as with whether or not public Christmas displays should be allowed, or whether saying “Merry Christmas” is a holier alternative that “Happy Holidays”) the scriptural record has little to say about knotty cultural problems. In the case of holy days, however, the Bible actually speaks up, although what it says requires interpretation.
If Senators DeMint and Kyl are sincere in their concern, they seem to be referring to a tradition originating in the Hebrew Bible (called by many Christians the Old Testament), wherein the Sabbath was set aside as a day holy to God and on which no work should be done. For Jews and Christians alike the Hebrew Bible has authority, but for Christians, a more authoritative question has to be, What did Jesus have to say about this question?