My son was like this, and the good news is that he wasn't kicked out of daycare. At 3 months, we started sending him to a wonderful Montessori school where they have been very willing to work through any problems. That said, we were on the verge of being expelled when he was 5 months old because he was so overly fussy. Fortunately, everyone hung in there and the situation gradually improved. Everyone is different, but he wasn't a happy child until well after he was a year old.
If I could do it over, I would expect less of him (as far as being able to do daycare) and would have stayed home with him a few months longer. If you are going to do daycare, I would recommend a setting where there is more than one person to care for her. If she is as frustrating as my DS was, you'll want to make sure that the care provider can walk away from the situation when needed and that there is another person in the room to prevent maltreatment. The school where my son goes has an open half door on the infant room. Kids, parents, and teachers are always looking in at the babies. In my opinion, this helps to keep everyone on their toes. There are also lots of other people around to jump in and help out in a tough situation.
Once my DS was able to do more things independently (ie. crawl, walk, feed himself, talk) his general mood improved. I also think my DS had reflux issues that caused pain. He grew out of this around 9 months. I understand the emotional and physical drain that having a needy child can be. Just hang in there, and remember that it won't last forever. My DS just turned two and is very happy, outgoing, and active.