Can I ask your thoughts on something? Just a little while ago I read: "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable rights, that among these are life, liberty and the pursuit of happiness. That to secure these rights, governments are instituted among men, deriving their just powers from the consent of the governed. That whenever any form of government becomes destructive to these ends, it is the right of the people to alter or to abolish it, and to institute new government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness."
There in the Declaration of Independence it says the people have the right to “alter or to abolish it, and institute new government.”
How does this tie in with God’s word in regards to Romans 13:1?
That is a question the founders of the United States struggled with for many years. Government are ordained by God, but what should happen when a government does not fulfill its duties as God appointed them? What was argued is that "Let every soul be subject to the governing authorities. For there is no authority except from God, and the authorities that exist are appointed by God" (Romans 13:1) was speaking generically of government, but was not addressing each specific government. I have to disagree with that line of reasoning since the statement was made while Christians lived under the Roman Empire, one that did not fulfill its duties to its citizens well, but which Christians still owed obedience when it did follow God's laws.
Another point, more accurately made, is to note from the Old Testament, the often people disobeyed the government laws when they conflicted with God's laws and under the direction of God had at times lead rebellions against the current government. Examples would be Daniel when he prayed in direct violation of a law, Ehud who murdered an occupying king, Jephthah who repulsed an occupying nation, etc. Obeying God instead of man is clearly defined, but today it would be hard to tell when God desires a people to rebel and form their own government. (Note that the founding fathers never believed in anarchy. They understood it to be God's will that governments exist.) "And He changes the times and the seasons; He removes kings and raises up kings; He gives wisdom to the wise and knowledge to those who have understanding" (Daniel 2:21). When God changes governments, it is done through the actions of people. Every change in governance came about by governments being toppled through wars or rebellions and God will be behind those changes. What the founding fathers decided was that England at that time was violating the laws of God. Thus they were in the right to rebel against those violations and they expected that God would support their cause.
Another point argued was whether it was the government's laws or the person ruling the government who was ordained by God. The founding fathers argued that England was ruled by a set of laws to which the king was subject. Thus the laws were above individual leaders. Yet the king of that time was violating England's laws. The colonists decided they were justified in insisting that England's law be upheld, even though it meant rebelling against the current ruler.
It should also be noted that there was never a time that the colonists, as individuals, gathered to decide to rebel against English rule. The colonies all had their local governments. It was these governments who took action against England when England did not uphold their own laws in the colonies. Thus for the Christian living in those times, they were always obeying their governing authorities. It was just that for a period of time the local authorities were in rebellion against the remote authorities.
Another fact often overlooked is that the early leaders spent about 11 years trying to reach a peaceful settlement with England. They did not take up arms against the government until after England sent its military into the private homes of its own citizens to seize property. The founding fathers felt they had no other choice but to defend their homes and they found justification for self-defense in the Scriptures. The Declaration of Independence came after the people found themselves attacked by their own government.