People often think that deep tissue massage will consist of me bearing down with my elbow, as hard as I can, until they cry uncle. That's really not a very productive use of massage, in my opinion. I see deep tissue massage as affecting the deeper layers of muscle tissue, allowing them to elongate and engage properly. This is best accomplished by warming up the muscles and then slowly working to deeper levels.
If you feel like you're trying to get away from my pressure, then your muscles are fighting back, and I prefer not to fight. I strive for finding a pressure that feels like a good stretch or good pain in the muscle- where it feels like a good hurt. Yes, sometimes it may reach a bit of pain level, but the rest of your body should be able to relax and allow the pressure. No matter who you get a massage from, you should always feel comfortable telling the therapist if you feel the pressure is too much. If the therapist doesn't listen, then they are probably not the right therapist for you.