Most people are forgetting 18 U.S.C. 926, also known as the Firearms Owners' Protection Act:
No such rule or regulation prescribed [by the Attorney General] 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.
Registries are currently illegal under federal law.
That said, how do we prevent one in the future? The argument many use is that they'll lead to tyranny. Comparisons to Nazi Germany come up, we veer into Godwin territory, and you lose the listener.
A better tack is to point out that implementation would be horribly expensive. Consider that Canada's registry was supposed to cost $6 million, all of which was promised to be paid for by registration fees. As of 2004, the actual cost was estimated at over $2 billion
The registries in Canada, Australia, and the UK have been failures, with compliance in each case hovering around 20%. They simply don't work.
Furthermore, there will be scads of cases in which law-abiding citizens get prosecuted for unwilling violations of the registry.