The Supreme Court has made lots of unconstitutional rulings. That happens to be one of them.
Requiring a permit is merely a time, place, and manner restriction, and may not be exercised in an arbitrary and capricious manner. Content may not be regulated. (This is why the Nazis were allowed to march in Skokie). Because free speech is a fundamental right, the regulation must be narrowly tailored to prevent the type of harm that may come from the speech-related activity, and the regulation must be no broader than necessary. This is the "strict scrutiny" standard that is used by Courts to evaluate whether or not a restriction on a fundamental right is overbroad.
Using this standard, I can't think of any harm that would be prevented by a national gun registry, as a registry will prevent no one from misusing their gun.
Thoughts?
Local law--not state or federal. Local government can do lots of things that state governments and especially the Federal government are forbidden to do. If your local town decided it wanted to implement a firearms registry, it is perfectly free to do so, however, as an instrument preliminary to total firearms confiscation, it is useless, as such confiscation would have to be nationwide have any effect.