I think almost every parent has gone through this same thing, or something very similar. I guess I would start by asking what time she goes to bed at night, and how many naps she takes during the day. She may be getting enough sleep for her age. If this is the case, you will need to either adjust her schedule, or adjust your own. I wonder if it's possible that she is a little afraid of the dark. When she's really tired, she might be too sleepy to dwell on it. But then towards morning when she's a bit more awake, it becomes an issue.
We found that a softly playing radio worked well for our son when he had this problem. We also did not give in to his wishes to get out of bed. We found that over time it worked to calmly tell him that it is not time to get up yet, laid him back down, and left the room. No matter how many times he got up and pleaded to get out of bed, my answer stayed the same. It meant that I lost some sleep in the process, but he got tired of hearing broken record mommy, and eventually started keeping quiet.
It also helps if you keep a very set schedule in general. Like you should plan on getting up everyday at 7 a.m.(or whatever is good) This would serve as the only acceptable time for your daughter to get up. That way, it the first couple days, when she might just not ever get back to sleep, you have a time when it's fine to give in. Also, a set nap time would help to enforce the new wake-up schedule. Try to keep her awake until her actual nap time, and if she's still asleep after a reasonable nap time, don't be afraid to wake her. She'll sleep better at night if she's not sleeping well during the day.
All of this seems a bit rigid, but that is what a toddler needs to feel secure, and learn the way life in the family works. It all really depends on how her specific sleep patterns are, though. It largely depends on if she's getting too much or too little sleep.