In my experience, Victoria T is right on. My older daughter (VERY independent, very stubborn, knows exactly what she will and will not do, thankyouverymuch) was totally pee trained in about 4 hours. No problems there. She resisted pooping on the potty though, and tried to hold it in, etc. Finally, I just waited until I knew she had to poop, and held her on the potty (I wouldn't let her do that arching her back to hold it in thing). I know, I know! So mean, so terrible, so not what the "experts" tell you to do... whatever, it worked. Once she realized that nothing bad would happen if she pooped in the potty, she was totally fine and went in the potty every time. No big deal. She just needed someone to make her get "over the hump" so to speak, and whatever fear she had of pooping somewhere other than a diaper just went away.
So, the method may be unconventional, but it worked. (She's turning 10 and doesn't appear to be scarred for life! ;)