One of my students recently had a problem with her son getting a little too smart about setting limits. He was understanding so well that he decided it was his turn! He'd say something like: "If I don't get to watch a video than I'm not going to..."
Mom was holding firm but was feeling like her resolve was slipping which happens to many of us all too often.
This is a power struggle that your child is trying to win with you. You do indeed have to hold firm! I would say something like "Nice try... and what did I say?" Or, "That's an interesting opinion, and when did I say you could watch?" When that doesn't work, what do you do? Say it again, very patiently. Repeat, repeat, repeat. Kids are trying to get us to lose our cool so that THEY win. When we can remember this simple technique we're capable of taking the struggle out of this equation.
You can also go Brain Dead and walk away.
Lastly, if your child is really not getting your point use good old Energy Drain to give a generic consequence. Something like "Gee, you really are draining my energy by acting this way. Why don't you put some energy back by taking the dog for a walk or weeding the garden? You can choose which you'd like to do before dinner."