A Christian’s Relationship With a Godless Government

Why should I “submit” to a government that I believe is moving in the wrong direction? I love my country and want to cooperate with the political system, but I’m struggling to understand what the Bible says on this subject. How in the world can the apostle Paul tell Christians to submit to the authorities (Romans 13:1-7) when we know for a fact that many human governments are corrupt and unjust? What should a believer do when he feels that his own government is “ungodly”?