Nothing. The M3 was not issued in significant numbers until 1943, too late to effect the war. The idea was to have a cheap and easily produced SMG to replace the expensive Thompson during the early phase of the war when production was not yet in gear. But due to the delay in development it never outnumbered the Thompson. Its competitor, the M2 Hyde was reputedly a better built and more expensive weapon. It was also unnecessary since it wouldn't have been available any earlier.
The advantage of the cheap stamped steel SMG was not very important to the American manufacturing giant since it managed to produce even expensive weapons such as the Thompson in large quantity. The American infantry also did not depend as heavily on this type of weapon as the Soviets and British did. Unlike those armies which were chronically short on rifles and sought to SMGs to meet the gap. The American infantry were lavishly equipped with semi-automatic rifles and even the cooks had carbines.