First, you'd have to repeal the 2nd Amendment. No small feat, but let's say you succeeded.



Next, as Jon Mixon says, you'd have to repeal the 10th Amendment. Without a 2nd Amendment the question of gun ownership would devolve to the state governments, many of whom explicitly guarantee a right to bear arms in their own constitutions. Without a repeal of the 10th Amendment the federal government would only have authority to ban the importation of firearms, or the trading of firearms between states.



After that, you'd have to repeal the 4th Amendment. The 4th Amendment guarantees that no unreasonable search or seizure shall proceed except with a warrant, and no warrant shall be issued except on probable cause. Since the federal government has no registration database of firearms, they have no way to know who does and doesn't own a gun. The only way for them to collect all the guns would be a house-to-house search of every home in America, and the 4th Amendment would immediately put a stop to that. So you'd have to get rid of it first.