The model which they were so happy to discover was the Machine Gun Tax Stamp from a few years earlier. Actually, the prototype for the National Firearms Act in 1934 (for a variety of firearms and firearm accessories) was the Harrison Narcotic Act in 1914.
If you read the Congressional record of committee hearings on NFA '34, you will find exactly this: the Attorney General assuring that it would be constitutional because the Harrison Narcotic Act had already survived scrutiny by the Supreme Court.
Weren't a lot of the Congressional debates about Marijuana and opiates laced with racism and xenophobia? I seem to recall reading posts talking about how Congressmen used scare tactics of dirty Mexican men high on the demon weed raping white wimmen. And Chinamen doing opium, probably raping white wimmen too.