This topic might also be extended to employer pressure as well....i have, but only very rarely, been subject to pressure from customers regarding operational aspects of a task. I find that easy to deal with, and in-fact it's simply part-and-parcel of the job. I have never had difficulty with a customer past that point once I've had my input to the equation.
What is fundamentally more difficult to deal with is employer pressure, which I see far more frequently than coming from customers. How to deal with that, whilst preserving your employment, is far more challenging with greater implications that just telling a client straight when faced with the same pressure.