Remember, even though you feel pressured to do otherwise, that your daughter and her emotions are more important than even a whole year of preschool. She needs to know that you are listening and supportive of her. Trust me, you don't want her to doubt that when she is 12! This support starts now. This is only a season, give her that time.
A couple of thoughts:
1) After listening and hugging her, see if telling her you will pick her up early that day will help adjust her - and do it. When you pick her up, say "How did you like me coming early today, did you miss the playground or was it ok?". Remind her that you keep your word and acknowledge her. You may be surprised what you learn.
2) Go in with her and stay awhile, maybe even leave with her after you play a bit. Afterwards, talk with her about the things in her class you enjoyed. Don't manipulate her by trying to tell her what she should have enjoyed and therefore should have wanted to stay (yes, we all do it :) ).
3)NEVER RUSH HER!!!! This the receipe for disaster. Be late, for gosh sakes, she is 3 :)!
4)When things get tough, keep her out for a day. Don't wait until the melt down happens at drop-off. Get in step with her and know if it is coming. When you do you know it is coming, prevent the melt down and reverse the day by saying: "Wow, I think you and I need to spend the morning instead of going to school. Will you be ok with that - I know you may miss xxxxx?" Try not to do it back to back days, but give her the opportunity to be heard.
5) She also may not be feeling well, even if she seems to be fine later. Right now, everyones immune is a bit activated. You may do some natural support (like cod liver oil or others) to help her get to top condition.
From another mom of a previously hesitant preschooler and a floortime play therapy trained mom - J.