Hi Mary Beth,
First, I would suggest picking up a copy of "Parenting with Love and Logic." This is a great book that will give you some really great ideas on how to handle this sort of thing and give you your sanity back. I use "Teaching with Love and Logic" in my high school classroom and it works great!
Here's how I've handled this. First, I begin with the assumption that my children need to do what I say, period. Explanations are a bonus, not required. (I do give them whenever possible, but I don't waste tons of time on them.) The only correct answer is "Yes, mom." Unless it's a question on how to do the assigned task, there's no discussion until it's done ("So, mom, one more time, how do I brush my teeth?"). If there is any backtalk, I toss out a pithy statement such as "I'm sorry. The complaint department opens at 3pm today. Feel free to gripe then, otherwise, do your task." Most of the time, my kid moves on to the task because he knows I'm a rock on this point (your daughter will need to learn this). The second (maybe the third, if I'm having a slow day), backtalk is met with wa warning of a loss of privelege ("Hmmmm...I can see you're not listening well. Very good. Let's free up your schedule by taking away [fill in the blank]."). The third time, privelege is gone.
BTW, three times is really a lot, but a good place to start out. At this point, my sons know they get one request and then we move on to consequences. For example, when my oldest was in jr. high, he "didn't feel like" doing his chores. Consequently, I "didn't feel like" driving him to the school dance (this followed a week of not feeling like chores).
The key to all this is staying upbeat, cheerful and firm. Say it with a smile! And don't engage in the discussion. When in doubt, repeat the task and the consequence. It can be anything, not necessarily a loss of privelege. I've been known to dish out additional chores, like weeding, cleaning closets or scrubbing tile grout if they get really awful. (I call this character retraining through chores.)
The idea is that your child will learn consequences to actions in a very immediate way. The worst it ever got in my house was my youngest son losing all priveleges, up to and including attending a birthday party, for a week because he chose not to clean his room when asked. I was sad for him, but he learned a very valuable lesson. Plus, it helped me cut down on the "I'm going crazy" feeling...my fuse got lengthened, if you know what I mean.
It's tough teaching this to kids (I do it every August and every January with my students), but once they learn they can't wear you down and that it's impossible to argue with your smiling refusals, they fall into line.
So, good luck, Mary Beth. I hope this helps.