The Civil War was the first time that conscription was used to enlist soldiers. It wasn't terribly popular for a few reasons. One was that the draft was viewed as an infringement on personal liberty. It also was perceived as an end-run around the Constitution by the military in an effort to gain control over the civilian population. It depressed morale in some units because of the perception that an unwilling soldier would be a poor soldier (which is also one of the arguments used against the draft today.)
There were so many exemptions to the draft, such as employment, "only son", commutation (paying a fee to avoid the draft) or hiring a replacement, that draftees tended to be immigrants or very poor.
The Draft Riots in New York City were the largest civil disturbance in the country's history.
I don't know how many troops were ultimately drafted, but I do know that, in the north, very few of those whose names were drawn actually served.