M.V.
As a teacher, I see this every year. 2-3 kids per Kindergarten class have this issue. It looks different for each kid, but the same thing works every time-make the break quickly, firmly, and lovingly. Some kids take longer to get used to the idea than others, but they all do. Pretty soon you'll be wondering what happened to the little girl who needed you so much. My own son was/is the same. He goes to a home day care for before and after school care, and he just started full-day kindergarten. Most days he says, "Love you, Mommy, you can leave!" Once in a while, though, he clings and cries. Those are the days his babysitter just pulls him off of me, I give him a kiss on the head, and I leave.
This process is harder on the parents than the kids, since the parents don't see the kids having fun a short time later. Stick with it though, and good luck!