This site gives a good account of the Union Draft in 1862.
"It is possible that the solution hit upon was a general call-up of more men, under the new militia law. On Aug. 4, Lincoln called up 300,000 men for nine months service, on top of the 300,000 he had already requested in July for three years. The militia call-up was General Order No. 94:
Ordered:
I. That a draft of 300,000 militia be immediately called into the service of the United States, to serve for nine months unless sooner discharged. The Secretary of War will assign the quotas to the States and establish regulations for the draft. II. That if any state shall not by the 15th of August furnish its quota of the additional 300,000 volunteers authorized by law, the deficiency of volunteers in that State will also be made up by special draft from the militia. The Secretary of War will establish regulations for this purpose.
Some confusion about this draft may spring from the fact that both the entire call-up of 300,000 militia, and the subsequent filling of the deficiency in that call-up by conscription, are called a "draft." This was not something that had been done in the lifetime of any of the men in the government, and their terminology was not always clear. Yet Lincoln unambiguously writes of "drafting," in reference to the filling of the quotas by conscription, in many places [e.g. letter to George P. Fisher, Sept. 16, 1862; telegram to McClellan, Oct. 27, 1862, etc.]
Like the earlier call, this one was apportioned among the states relative to their populations. But this time, the government said it would draft men into service from any state that did not meet its quota. Specifying that the call-up would be for nine months, and calling the troops "militia," gave it the power to do so.
The War Department order gave each state until Aug. 15 -- a mere two weeks -- to meet its quota or face a draft. Indiana's quota was about 21,000; little Rhode Island's was less than 3,000. New York's quota of almost 60,000 men was the highest. Wisconsin's was just under 12,000. The governor there pleaded for more time, since it was an agricultural state and the fall harvest was approaching, but the War Department only gave him another week, until Aug. 22.
On Aug. 9, the Secretary of War issued General Order 99, detailing how the conscription should be handled. It directed the governors to enroll all able-bodied men age 18 to 45, and the wheels of the draft began to turn.
The process passed down the line, from federal government to states to counties to the smallest unit of local municipality. The legwork was done by the county assessors, the men who usually collected tax data. They copied the names of each eligible man into record books, noting those already in service, and any obvious physical disabilities. The Pennsylvania enrollment officer in one township evidently hadn't appreciated the random nature of the draft, or else couldn't resist adding editorial comments on some of the men he registered -- "Ran and hid, refused to give age;" "Ought to be taken. Bad influence at home or he would volunteer," "Not healthy ('So they say')," "claims weak eyes," "Saucy & loafing about at home," "Make a first-rate soldier, not worth much for anything else," and so forth."
http://www.etymonline.com/cw/draft.htm
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