It's an idea that seems to be gathering a bit of steam.
At Forbes.com, John Wasik lays out the logic behind treating firearm deaths as a market externality to be compensated via insurance, as we do with cars: "Those most at risk to commit a gun crime would be known to the actuaries doing the research for insurers... An 80-year-old married woman in Fort Lauderdale would get a great rate. A 20-year-old in inner-city Chicago wouldn’t be able to afford it. A 32-year-old man with a record of drunk driving and domestic violence would have a similar problem."
Robert Cyran and Reynolds Holding write that mandatory liability insurance is a measure that could pass Supreme Court muster where other restrictions might fail: "[T]here’s a strong argument that damage caused by firearms gives the government a 'compelling interest' to require insurance, the test for infringing a constitutional right."