Let's read Romans 13 which is something that will prove helpful. When we hear the word "authorities" we think primarily of pompous men who execute their will through the keys they have received, but that is not what Paul meant by this word at all. The Doctrine and Covenants, in a similar way, says that governments were instituted by God, which in totalitarian cases, like the Nazis, would be obviously absurd. But the Doctrine and Covenants has no specific government in mind. Rather, when it speaks of governments, it refers to the tools and methods of government.
When Paul says "authority" or "authorities," he likewise makes no references to specific office holders but to the abstract placement and operation of the tools of governing. It is the idea of authority and the bedrock notion of government that is being discussed in these passages, not whatever abusive personality might manage to get hold of their reins.
When read in that light, the meaning of what Paul wrote, now located in Romans 13:1-7, becomes crystal clear. It is the idea or notion of government that is not to be despised because the whole concept of government comes from God. He placed it in our bosom. When you refuse to govern----when you vote so as to close down government----you are resisting that which God has appointed (as Big Money always does), and you show dishonor to your nation. Why? Because government is "not a terror to good conduct but to bad." Those who want to engage in bad conduct will always want to close down government and do away with regulations (Mormons, see 3 Nephi 7:6).
And that is what the Tea Party is now about. They may well evoke the image of the common man and they may even give lip service to the common good, but the only thing common about the insurrectionists in the House of Representatives (and the Senate, let's not forget Mike Lee) is their unyielding lust for money and power.