Haynes v. United States
might not be the best argument against registration. The court ruled in Haynes' favor because, in his case, registering his gun would have been an act of self-incrimination.
A better argument is found in the 1986 Firearms Owners' Protection Act:
No such rule or regulation prescribed after the date of the enactment of the Firearms Owners Protection Act may require that records required to be maintained under this chapter or any portion of the contents of such records, be recorded at or transferred to a facility owned, managed, or controlled by the United States or any State or any political subdivision thereof, nor that any system of registration of firearms, firearms owners, or firearms transactions or disposition be established. Nothing in this section expands or restricts the Secretary's authority to inquire into the disposition of any firearm in the course of a criminal investigation.