If somehow the miracle of passing an amendment banning guns occurred, I think you'd be in for a real possibility of armed conflict. LEOs around the country would not want to enforce such a law, for reasons of their own personal safety, or because they would never support it. Further, there is no national list of firearms, so there's no way to know who does and does not have a firearm. Short of house to house searches, I don't know how you figure that out.
People would likely turn in their firearms, but they'd be in the vast minority. I wouldn't turn mine in. I don't care what psycho babble you use on me regarding peace and love and unicorns - if I know bad guys are keeping their guns, you can rest assured I'm keeping mine to protect my family.