Two year waiting period, anyone?
The lack of a waiting period is relevant to gun control in general, but not to this case unless the story author is proposing a period of over a year.
He's correct that Republicans and the NRA are cherry-picking the US Constitution, but a devil's advocate can find instances of Democrats and gun control advocates doing so in the opposite direction. For example, arguing that the 2nd Amendment is obsolete due to changes in technology could open the door to similar arguments about the 1st. (You no longer need to stand on a soap box, and the number of people you might be able to incite is orders of magnitude larger.)
What's missing from both of those arguments is that enforcement has also improved. The violence we currently have in the US is not even remotely close to what he had when the National Firearms Act was passed. An even more dramatic change is how effective enforcement agencies have become at catching people who commit it. A thug in the 1920s could kill occasionally and get away with it for years; now someone with a grudge has essentially no choice but to do as much damage as possible in an hour because the SWAT team will be there by then.
It's also hard to come up with an argument for gun control that isn't an argument for alcohol prohibition. When you tally the murders and domestic violence incidents in which the attacker was drunk, rapes involving the same, fatal accidents and cirrhosis deaths, fetal alcohol syndrome and associated violence, and traffic deaths, the human cost is similar and maybe larger.
There are also few people who could claim a genuine need for ethyl alcohol under the strict standards that are used for gun ownership in many places. (Pick a utilitarian application for it, and there's a better, safer technology: portable water-makers and -purifiers, refrigeration, safer preservatives, non-abusable oral disinfectants and better mechanical cleaning methods.)
I enjoy a Newcastle now and then, so I'm simply pointing out that the public-interest arguments used by gun-control advocates would make it hard to defend my freedom to do so. I don't really *need* it, and the ready availability of liquor (with no waiting period and no background check for past drunk driving convictions - even fatal ones) costs perhaps 50,000 lives in each year in the US.