Cindy -
yes, totally normal. Which is crazy, that this behavior can be considered normal!!! But anyway, I don't know why they call it the terrible 2's - mine started at 18 months, he's 2 1/2, and my talks with parents of 3 year olds don't give me much hope there, either.
What made (and still makes) me feel the worst is just that rejection, and how do I deal with it. It makes me feel instantly incompetent as a mom. I swear, everyone else is doing this so much better than I am, right? So while you will not be able to really change her behavior (she needs to go through this phase), you can change how you respond to it. You can fake control, if you will. I do this by not asking my son questions that he can answer yes or no, but rather just involving him, so if he sweeps everything off the table in one swoop, I start to clean it up and just chat to him as if he's expected to help me, too. If he says no (what do I mean if....WHEN), then I try to turn it to a game, asking him to pick up everything that is blue, or something like that. Sometimes works, sometimes doesn't, but I feel better when I don't engage in that battle of wills (because I feel like I always lose, no matter what happens). Most of the defiance is just a test of independence, anyway, and I'd rather not start those battles over trivial matters for a few years. I Tivo all Supernanny episodes so I can remind myself that there are lots of parents who are a lot worse off.
Some of the frustration also comes from not being able to express themselves verbally (which comes all too quickly in the next year). And they have all that energy. So they just throw down into cringe-inducing tantrums that are hard to ignore. When this happens, I do something kind strange...I have this weird looking doll that someone gave me as a stress reliever - it has crazy hair and you're supposed to whack it when you get frustrated. So my son would start a tantrum and I'd just go get this doll, come back and start whacking it on the ground next to him. It would freak him out, then he'd laugh, then I'd talk to him about when he's upset he can go get this doll and whack it on the ground. He giggles and giggles about this, and sometimes now he'll get the doll and whack it. Not sure if this little method actually helped him, but it did help me. A lot. And then I would also go in another room and whack it myself!! :)
Suffice to say, at this age, nothing you do will seem effective. Everyday you will have to gear up for this, and every night you will feel you failed, and every once in awhile you'll get cooperation and it will give you little glimmers of hope. Hold on to these glimmers! You are getting through to her, just as she is getting through to you.
And if it's any consolation, from what I hear, the cliche is terrible at two, terrific at 16, and terrific at 2, terrible at 16. I would so rather deal with a terrible two than a terrible 16. (Not sure how true this is, but an informal poll of my friends seems to hold up this theory, so I'm just counting my blessings and doin' my time....)
Good luck! S.