From Law and Liberty:

An analogy to the First Amendment demonstrates why the delays in gun access are unconstitutional. While the First Amendment permits states to require licenses for demonstrations (because of the need to prevent disruption to other activities), such licenses cannot be so unreasonably delayed as to effectively undermine the right of free speech. Moreover, the First Amendment suggests the need for licensing exceptions for demonstrations in response to breaking news. In any event, judges have permitted short delays of only a few days before licenses for demonstrations must be issued.

Similarly, licensing is permitted under the Second Amendment to make sure that guns do not get in the hands of felons and the mentally ill—categories of people the Supreme Court has stated do not have the right to guns. But delays in issuing gun licenses during unrest would render the Second Amendment right as ineffective as unnecessary delays in protest licensing would the First. Moreover, substantial delays are unneeded to determine whether someone is a felon or has been adjudicated as mentally ill, as the federal instant gun check program shows. These delays are also far more substantial than any “cooling off” period that would help prevent crimes of vengeance or passion, even assuming that such a reason for delay was compatible with the Second Amendment’s provision of a right to ready self-defense.