As Christians in America, we have a unique challenge with regard to the command in Romans to “Let every person be subject to the governing authorities.” We live in a culture where the people in political office were selected by us.
Until Saul, God’s people lived in a theocracy. Saul, David, and Solomon were human kings chosen by God. Since then God has stepped out of the direct choosing, apparently opting instead to turn all things to His good, regardless of how a given leader was put in place.
Unless I’m mistaken, the only form(s) of human government mentioned at length in the Bible were monarchs (and perhaps judges and prophets, depending on how one defines government).
Despite the fact that, by the time of Jesus, democracy was well established in Greece, the Bible makes no mention of this as a form of government sanctioned by God.
In America, democracy takes the form of a democratic republic - representatives are chosen by the people to hold the various offices. This is true of legislators and of the president. So, the president is not the authority in the traditional sense. He is selected to represent the people by the people, themselves.
Add to this the fact that there are three branches of government, which are intended through checks and balances to be of equal power, then it can not be argued that the president is the leader or ruler.
As Lincoln pointed out, we are a government of the people, by the people, and for the people. It’s difficult to imagine a more stark contrast to a monarchy, where the royal “we” is frequently invoked and it’s understood that the king or queen IS the country - basically relegating the populace to vassals of the monarch (which is, in fact, the legal situation).
So, if we are (Note: not “if we have”; but “if we are”) a government of the people, by the people, and for the people . . . if the people who hold political office (as public servants, by the way) are there to represent the people . . . even assuming we all agree on what it means to be subject to the governing authorities . . . then the question becomes, “To whom do we owe this subjection?”