All the laws of the United States and the respective States flow out of the Constitution. If the Constitution were destroyed or made ineffective, all the laws of the United States would go down as well. What would the effect of this be?
First, the United States is NOT America. If the United States Constitution went down, or if the United States itself went down, the people would still be there. The only difference would be, the people would take up their individual authority.
Read the Preamble to the Constitution:
We the people of the United States, in order to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity, do ordain and establish this Constitution for the United States of America.
Break this down a little. When there was no Constitution, and then some people ordained one, how could they be people of the United States, if the Constitution is the thing that FORMED the United States? They couldn't. The United States was in existence BEFORE the Constitution. And the people gave up none of their authority to the Constitution. Just the opposite. The Constitution was set up "to form a more perfect union, establish justice, insure domestic tranquility, provide for the common defense, promote the general welfare, and secure the blessings of liberty to ourselves and our posterity." In other words, the Constitution was set up to strengthen and benefit the people.
If the Constitution goes down, the people remain, the United States remains, and common law reigns. What is this common law? It is, "Do no harm to your neighbor, do not injure him by damaging his property," and don't break your contracts you have with him, which is harming or injuring (damaging his property) him.
What would be the court system? It would be the process and judgment of the local area in which people live. The jury was set up long before the Constitution came into existence... based on the common law of England, which goes way back to even before the Magna Carta. It was in use in America way before the Constitution came into existence.
In other words, if we don't pick up the common law that we have to use, it just might be better to replace the Constitution with a document that makes the common law the formal rule, so that government people can't use government to harm the people any longer.