Tell the new employer you can start in two weeks because you want to give Target the courtesy of two weeks notice. If they want you right away, do as sbrando7 said, and see about Target cutting you to weekends only for two weeks and your new employer working around it. If the new employer balks at either of those options, be careful, it could be a red flag of what type of employer they will be. If they can work with either of those options, talk with Target HR, give your notice to them and on Workday, work your scheduled two weeks, and move on. Target may seem like a small bridge to burn at this point in your life but you want to keep all your options open because you never know what the future may hold.
In the end, do what your gut says is right, and good luck with your future!