I was watching Band of Brothers for the nth time recently, and in his interview, (I believe) Carwood Lipton said that a few men in his town committed suicide for being 4f. If men were willing to kill themselves becuase they couldn't even serve in the lowliest, non-combat roles, why would the draft even be enacted? Support for the war obviously swelled in the United States after Pearl Harbor and the declaration of war by Germany. Did the Roosevelt administration feel that not enough men would volunteer?
So a few competing things that bear examination here.
Is that the draft as it were actually began well before official US entry into WW2.
As the war began to go poorly for the Allies, and especially with the defeat of France in June 1940, Americans began to feel more keenly how unprepared and small particularly the Army and Army Air Corps was. Thus in 1940 Congress passed and FDR signed the Selective Training and Service Act of 1940. It established the first peacetime draft in US history and was designed to slowly build the US military, and establish a trained cadre of troops to ease expansion in the event of war and raise general readiness. It required the registration of initially men 18 to 45 and at first 1 year of service and no more than 900k men in the process at any one time.
Was that in early 1942 for most men ALL voluntary enlistment was ended. In the weeks after Pearl Harbor the rush to join up overwhelmed the prewar infrastructure, and particularly the uneven nature, since nobody wanted the crap jobs.
Thus to better control the influx and react to the needs of the services everything was funneled through the Selective Service Administration. That way if the Army said they needed 5000 truck drivers, and the Navy 2000 radar operators next month then the SSS could call up the men categorize their skills and the branches could find the people they needed, or tell people what they were going to be doing.