Change can take a while, but 6 is a great age for daycare. It's like a play date, and for social little girls, really fun. My daughter usually refuses to leave!
Still, it will take a while for her to make friends and get used to the change. First, be confident in your choice. If you cannot be, consider if you made the right one. Your daughter will pick up your unease and play to it. Second, encourage her to make friends. Are there any children at daycare that are also in her class at school? If the other children have been together a while, and she is the new one, she may be having trouble breaking in (remember that little girls can be quite mean). Third, sneak little notes and photos into her backpack so that she knows you are still thinking about her. Keep them positive, so that they don't end up playing into any of her insecurities.
My two children usually do after-school care a few days a week, but more when I have work deadlines. I LOVE our daycare. More often than not my kids will complete their homework at daycare with their friends, so that once home we can enjoy family time. But how happy they have been on any given day does depend a lot on what happened socially. Was a good friend there that day, and did that good friend play with them? Things like that. So keeping my pulse on the social aspect is important to making sure they have a positive experience.
Making play dates outside of daycare with kids who attend full time can be difficult, as the families are going to treasure their family time, but if it is a short term thing, to help your daughter ease in, it can probably be arranged.
Finally, don't let a few tears worry you. Your daughter is expressing herself, what her preference is, and she has every right to. But those tears are gone the instant she sees a friend to play with, I am sure. Stay upbeat and confident, and she will, eventually, also.