So a couple of things going on here:

1st, the 1934 NFA did not BAN anything. Especially not machine guns.

It imposed a duty to REGISTER them with the Secretary of the Treasury and pay a $200 tax stamp on them.

This was because the weapons covered were being used in crimes and to outgun the police forces of certain areas, so it was thought that by requiring registration and by imposing what at the time was an EXPENSIVE tax stamp, Congress could effectively ban such items.

This... worked... sort of. I like to be very careful with political issues that are still very relevant, but suffice to say that overall the NFA DID reduce the number of the SPECIFIC types of weapons that are named in it, but it's actual effects on crime and other issues as stated by Congress at the time are much more controversial and debated.

The political climate in 1934 was very supportive of the idea of such an act because of things like the St. Valentines Day Massacre, and the attempted assassination of President Roosevelt.

But, by 1938 the United States District Court for the Western District of Arkansas ruled in the now semi-famous Miller case that the act was unconstitutional and directly violated the 2nd Amendment.

However, and this is why this case is only sem-famous, Miller lost on direct appeal to the US Supreme Court due to very controversial circumstances.

Which is to say, he was murdered before the Supreme Court could hear his arguments the next year.

Also he wasn't likely to hire a lawyer because he was a known bank robber who was going in to hiding right after the trial.

So the Act was ruled constitutional in US v Miller, though it had some problems later, but yes, as soon as 4 years after it's passage there WERE 2nd amendment concerns that were upheld by at least 1 Federal judge, though possibly with ulterior motives on both sides.