I Was Wondering? What if man’s law conflicts with God’s Word?

There is a natural rebellious bent to the human spirit; we often resist authority, and fail in our understanding of submission.  Even for the Christian, the residue of subversion often remains, and requires God's Word to teach and instruct us how we are to submit to our governing authorities.  But what should be the Christian's response when our government conflicts with God's Word?  How has Jesus modeled THAT kind of submission for us to follow?