Tanks and healers are in general top priority, you could do with a dps less but losing a tank makes most fights impossible and losing a healer puts more stress on the other healer(s) still alive, which then could force them to let people die because of the damage being to high for them to handle.
It's an interesting question in a lot of ways.
In practice, I find that my healing algorithm is to focus on the tank and then handle the raid when I have a moment. Thus it's usually not all that conscious of a call to let a dps die. If the tank is below 50%, the tank is getting my next heal, and there's nothing to think about. I only make an exception for wild growth, which is so powerful you've just got to hit it on cooldown if you've got an opportunity to use it.
A related question is when do you battle rez someone? I run into this question all the time in raids if a dps dies early on. If I rez them, then we'll have a lot more dps, but I'll waste the fight's only battle rez. (I mostly run in 10-mans). Maybe we'll have an emergency later on? Deciding when and who to battle rez is often a more concious and interesting choice.
Most of the time, I won't battle rez a dpser. However, if the enrage timer matters for us, I'll do it. If that dpser was performing some vital role and not just nuking the boss, I'll do it. Also, counter-intuitively, I'll also battle rez dps if the content doesn't seem that challenging. In such cases, I figure we don't need the battle rez for the purposes of defeating the content, and it's more of a social issue of whether to leave a fellow player laying on the floor or not.