They way I understand it, is they want to ban assault weapons because they are the easiest ones used to convince people. That would be the first ban. The NFA in 1934 didn’t ban weapons, it regulated them. Once assault weapons are banned, and the ban holds up, then it’s just a matter of expanding the list to add more guns until eventually they are all banned.
There's a reason special ops forces use M4 carbine or other equivalent "assault rifles" instead of Winchester 70s, lever action marlins, or even M1 garands.