@horses: In most states, if you are enrolled as a full-time college student, you are ineligible for unemployment pay. You would likely be disqualified based on that. Since Target knows about your school status, they will bring it up as part of their response to your UI claim.
I'll be more explicit than normal: work can suck! All jobs have moments when you put up with horrible sh** and abuse. Sometimes every day feels like it's horrible sh** and abuse. For the vast majority of us, our current jobs at Target are generally okay but not our "dream job" or "dream company". We learn to put up with the unpleasant stuff, menial tasks and unfair management politics, build a positive attitude toward ourselves while we are at work, and most importantly (laugh at this if you like) bring a smile and some enthusiasm to work, particularly when we are working with guests (the public).
If you remain employed, and use as much of your spare time as possible in conducting a job search, you might find a better position at a place you would like to work at.
Quit your job ASAP if you insist, but don't expect to receive any unemployment money or to easily get hired for a "better" job after you've just quit one.