Poop training often follows pee training by weeks or months. The whole process is considerably different than peeing, and more complicated for littles physically, and sometimes emotionally. Children have very little opportunity to control their lives, so eating and potty training, which they can and do control, can quickly become the most obvious signs that a child's frustration or fear levels have been exceeded.
I hope your potty "pre-training" messages have been positive and supportive, which usually gains healthier compliance than a parent-imposed deadline. If a child responds by withholding (which can seriously complicate the issue if the child develops painful constipation or worse, encopresis), parents have only a few choices: back off the deadline, change tactics, or scale up the pressure and hope for the best.
If I were in your position, I'd choose backing off AND changing tactics. If I hadn't already introduced the book Everybody Poops to my child, I'd do that right away – it introduces a positive, humorous tone to the learning process. Backing off feels like a "fail" to lots of moms, but it doesn't tend to confuse children; rather, it gives them more time to sort out the urges and sensations and responses, and reduces their anxiety. I know you are eager to get your daughter trained, but at three years, even 2 or 4 more months allows time for tremendous physical and emotional development. It can make a significant difference in her ability to succeed without undue stress.
If for any reason you simply cannot wait for her to learn this new skill, you might try this process, which has given a number of moms I know a lower-stress means of coaxing their children to try: http://www.rogerknapp.com/medical/pottytrainingrefusals.htm.
Wishing your family success and happiness!