have all Congresspeople sworn in on the US Constitution -- the document that they are supposed to uphold.

It seems these days that politicians cannot tell the Bible (or other religious text) from the Constitution in terms of what they are meant to uphold. If members of Congress were sworn in on a copy of the Constitution, perhaps it would help remind them that it is the country that they are supposed to be serving, not legislating by their religions. They should swear their oaths of office to the country and its citizens, not to any deity or deities.