The general framework is straightforward and certainly well-known to those who have studied (let alone taught) constitutional law. The government cannot abridge constitutionally protected rights simply to make a symbolic point or because it feels that something must be done. Any measure must be justified by a legitimate government interest that is compelling or at least important. At the same time, any regulation must be "narrowly tailored" to achieve that interest.
Several states, for example, are considering gun-insurance mandates modeled after those for automobile insurance.
There is no conceivable public-safety benefit: Insurance policies cover accidents, not intentional crimes, and criminals with illegal guns will just evade the requirement. The real purpose is to make guns less affordable for law-abiding citizens and thereby reduce private gun ownership. Identical constitutionally suspect logic explains proposals to tax the sale of bullets at excessive rates.
The courts, however, are no more likely to allow government to undermine the Second Amendment than to undermine the First. A state cannot circumvent the right to a free press by requiring that an unfriendly newspaper carry millions in libel insurance or pay a thousand-dollar tax on barrels of ink—the real motive, in either case, would be transparent and the regulation struck down. How could the result be any different for the right to keep and bear arms?