When the National Firearms Act of 1934 was passed, pistols with shoulder stocks were not mentioned. Short barreled rifles were not intended to be in the law. They were inserted at the insistence of a confused congressman on the House Ways and Means Committee.
Fitting a pistol with a shoulder stock had always been an option. The 1934 NFA was imagined to be regulating shotguns which had been shortened to create concealable, awkward pistols, not pistols that had a stock added to them, creating a carbine more accurate, but less concealable than a regular pistol.
The primary targets of the 1934 bill had been pistols, revolvers, sawed-off shotguns, silencers, and machine guns. Through lobbying by the NRA and concerned citizens all over the country, pistols and revolvers were taken out of the bill.
The resulting law regulated things most people did not have.
Homer Cummings was the first Attorney General of the Franklin Delano Roosevelt (FDR) administration. Cummings pushed hard for national restrictions on firearms. He had a long run as Attorney General. Cummings helped engineer the U.S. v. Miller test case of the law before he left office in 1939. Cummings is credited with many of the laws which vastly expanded Federal power in criminal matters.
The economic failures of the New Deal, and then World War II, removed most interest in the National Firearms Act. For many years, there was little enforcement. Returning servicemen brought back war trophies of shoulder-stocked Mauser and Luger pistols.
Click the link to read the whole article: ATF Stocked Pistols “Short Barreled Rifles” in 1961