Every person is to be in subjection to the governing authorities, for there is no authority except from God, and those which exist are established by God. Romans 13:1
For every person who is in authority, God has some reason for allowing him to be there. We may not understand how that person is part of God's bigger plan, but, really, is that anything new? God has always done things we don't understand and He'll continue to do so. He gets to do that because He's God.
Because God is the One who has given our leaders authority, we are to respect and obey them.
Notice also that this verse doesn't say we only have to obey leaders we consider to be Godly. It doesn't say "Godly authority", it just says "authority". Sometimes it's tough, but out of love and trust for God, we must respect and obey our leaders.
That thought shouldn't be a frightening one for Christians. One of the bedrock principles of our faith is that God has promised to take care of those who love and obey Him. We might experience some "momentary, light affliction" (II Corinthians 4:17) in the process, but in the end, whether on earth or in Heaven, everything is going to turn out ok. More than ok, fantastic.