The effect of declaring some activity as being protected by a constitutional right is to remove it from democratic politics. If the activity is expressing dissatisfaction with the government, then the people, acting through their government, cannot suppress such expression. If the activity is owning a gun, then the people cannot suppress gun ownership. When the people, acting through their government, try to regulate the activity in question, the court says "no way!"
It is easy to understand why certain political freedoms should be put beyond the arena of politics and be protected by courts. Without such rules, the party in power can entrench itself and undermine political competition. It is hard to understand the analogous arguments for constitutionalizing gun rights.
Some argue that if people do not own guns, then democracy is put in danger, since people can no longer take up arms if the government tries to establish a tyranny or refuses to protect them. Maybe this was a legitimate concern at the end of the eighteenth century (or even the nineteenth century, as Akhil Amar suggests ), but as a theory for restricting democratic politics today it is farfetched. Gun owners are politically powerful; gun control laws are few and limited; gun rights are endorsed by both parties; with hundreds of millions of handguns in circulation, no serious gun control law has a chance of success; and, even if everyone were disarmed, the government would not impose a dictatorship. It already has more than ample firepower if that is what it really wanted to do.
Others argue that governments fail to protect people from crime, so they shouldn't be permitted to deprive people of the means to protect themselves, as this would violate a right to self-defense supposedly found in natural law. But your natural right to protect yourself with a gun comes into conflict with my natural right to protect myself by disarming criminals; this conflict can only sensibly be resolved through political compromise. The government's crime policies are political choices; if arguments against gun control are plausible, they have a fair chance in the political arena--and indeed have won the day virtually everywhere.
Finally, a number of people argue that gun rights are "customary" or "lived rights." If so, so much worse is the case for constitutionalizing them. If gun ownership is such a profound part of our culture, any government that tried to restrict it without very good reasons would pay a high price at the polls.
There are plenty of reasonable policy arguments on both sides of the issue, but these arguments should be directed to legislatures, not courts. There is no plausible argument grounded in reasonable constitutional theory for taking gun ownership out of the arena of democratic politics.