"My service is still not working. My business depends on the reliability of this website and if this can't be fixed I'll have to switch providers immediately."
Do customers think support people are more inclined to respond faster if they include a line like this? Do they subconsciously think a slight threat is going to get their problem fixed any faster?
The unfortunate fact is that 99 out of 100 times, the "problem" is a user error (at least in our case - in this particular instance, a misconfigured domain name). But when you're the service provider, it's never the customer's fault -- and I'll gladly take on their problem as if it were the most important thing in the world, but because I want them to have a good experience, not because of their tone.
There's just something inside me that hopes they don't correlate their slightly threatening tone to what got their problem resolved, because it really doesn't help.