Sometimes, negative utilitarians will attempt to promote their system with a particular type of argument. For instance:
"No amount of happiness enjoyed by some organisms can notionally justify the indescribable horrors of Auschwitz." 
The implication is that happiness, joy, ecstasy cannot have weight or moral importance in the same way as suffering, misery, and agony do - for, if they did, it would be the case that
They would, instead, have us believe
(1) Any amount of suffering can be outweighed by a sufficient amount of happiness.
It is clear that (1) and (2) are mutually exclusive; to find an amount of suffering that cannot be outweighed by happiness would be to prove (2) and disprove (1). I believe that this is what the negative utilitarians attempt with Auschwitz-style arguments. Here's why they fail...
(2) There exists some amount suffering which cannot be outweighed by any amount of happiness.
The horrors of Auschwitz, as presented, are indescribable. I suggest that they are amongst the worst imaginable, or that we are to think that they are. So - grant me this - there is some amount of suffering, Si, which is the largest amount of suffering that we can imagine. [1a] The suggestion, then, is that this amount, Si, fulfills (2) - for we can imagine no amount of happiness that can outweigh it. I will grant this - there may be no imaginable amount of happiness that can outweigh Si, nor, perhaps, the horrors of Auschwitz. Do I then forsake (1)? I do not! I maintain simply that the amount of happiness required to outweigh them may be unimaginable.
I also notice another claim:
This claim is also made by negative utilitarianism - it is, naturally, compatible with (2) and incompatible with (1). For (3) to be true,
(3) No amount of suffering can be outweighed by any amount of happiness.
must be false.
(4) There exists some amount of suffering that can be outweighed by an amount of happiness.
A simple thought-experiment: I can imagine some trivial pain - for instance, stubbing my toe getting out of bed.  I'll admit, I have not known much joy in this life - but that I've had I treasure very highly. If I was deprived of all my life's joy, in the prevention of this toe-stubbing, I would feel that to be a very great wrong done to me indeed. For those who disagree, I suggest that either they've not known joy, they've known it but blocked out the memory, or that they are otherwise attached to negative utilitarianism. Short of paradise-engineering, there's not much that I can do for those of the first two sorts,  but I hope to show why an attachment to negative utilitarianism is unnecessary.
Let us reconsider the claim (1), that suffering can be outweighed by happiness. I would make a simple point - that suffering can be outweighed by happiness, does not imply that in any given situation it actually is. What I mean is that the amount of pleasure required to balance a given pain is not dictated... it could be large or small without limit. We could say that the value of the suffering of a day in the life of a certain being is -1000 (in whichever units we are using), and that the value of the happiness of the being on that day is 0.001 (same units) - the disvalue of the suffering is a million times more significant than the value of the happiness. And we can say this if the being is a man is a torture chambre, an ordinary 20th century businessman going about his normal routine, or a wireheaded rodent in an orgasmic lever-pressing frenzy (who happened to stub his toe before reaching the lever). These are all consistent (classical) utilitarian positions. 
So the man who would give up all his life's joy, rather than have it contain also the slightest degree of suffering, can do so from a classical utilitarian position - the negative utilitarian position is functionally equivalent to a certain type of classical utilitarian position - a position where pleasure holds very little value. If the amount of pleasure required to balance a certain pain is a variable, then the view of the utilitarian steadily comes closer to that of the negative utilitarian as the variable increases - they will agree on more and more matters as to what is right and wrong. And there is no dividing line, just a continuing trend... eventually they will agree on all practical matters. This variable would mark out a scale - the further someone's position on the scale, the more negative their philosophy (at infinity, they would be a negative utilitarian). Every utilitarian, unless he counts pleasure as supremely valuable and ignores suffering, will be negative to some degree. I, myself, would in this way be a quite strongly negative utilitarian - I take the main duty of today's society to be the reduction of suffering.
Perhaps I will now be accused of perverting the meaning of "negative utilitarian" - whereas before it had a clear and distinct meaning, it would now, by my usage, admit of degrees and perhaps cause confusion between the different meanings. If this be the case, I urge the philosophic community to quickly agree on some new name for this feature that I have described (for it is surely very useful) - a property whereby a classical utilitarian can be to some degree similar to a negative utilitarian. And, of course, vice versa.
1. David Pearce, The Hedonistic Imperative, section 2.7. Perhaps this specific comment is meant more as an indication of the implications of negative utilitarianism, rather than a persuasive argument in favour of it, in which case this is a bad example.
1a. I do not mean that we cannot image a scenario which if it were real would contain more suffering (than Auschwitz or Si), only that while it is imagined it would seem no worse - that our ima
gination fails to appreciate value beyond some limit:
2. The negative utilitarian may answer that this pain is so trivial that it involves no suffering. But he must admit that suffering occurs in degrees, and I will substitute any small harm involving a tiny degree of suffering for the above. Or will the negative utilitarian suggest that there is no small amount of suffering - that all negative conditions are in practice one of either trivial discomfort, or terrible torment, there being no conditions inbetween?
3. Probably strongly introverted neurotic personalities, quite unlikely to be stable sensation-seeking extroverts - see chapter 14 of "Mindwatching" by Hans and Michael Eysenck.
4. That's an exclusive "or" - I do not suggest that the value of suffering and happiness is the same in each case, only that, for each of these situations, there exists a consistent classical utilitarian scheme that would assign those numbers (-1000, +0.001) to it.