So, here are a few things to ask about, for both sides, whenever your opponent assumes or glides over them. Note: these are not the questions themselves. Frame your questions for strategic advantage; see the example below, and this note.
1. What justifies criminal punishment? Who determines what proper punishment should be?
2. What limits punishment, if anything?
3. What is the nature of the society in the resolution? Will the outcome change if the society is democratic, authoritarian, or a constitutional monarchy, among many other options?
4. Why are illegal drugs illegal?
5. What does abuse mean? Is it mere misuse, or a pattern of sustained, debilitating misuse?
6. What are some of the potentially distasteful options for public health treatment?
7. What are some empirical examples of nations or governments that have tried a public health approach?
8. Does the phrase "illegal drugs" include legal drugs used off-label or without a prescription?
9. Is there an agreed-upon approach in the international / medical community?
One of the primary goals of CX is to expose the flaw or weakness in the opposing advocacy, which is why one of the best CX techniques is a species of reductio called the reductio ad ridiculum or reductio ad incommodum. Here's an example.
AFF: Your criterion is utilitarianism, correct?At this point, the Affirmative has given the Neg several awkward choices.
AFF: Under that criterion, how do we justify criminal punishment?
NEG: By measuring its effect.
AFF: And how do we do that?
NEG: By looking at whether society is overall improved.
AFF: But that's hard to do, isn't it, when you have an essentially harmful response to a harm? For instance, how does it improve society to imprison drug abusers?
NEG: I guess I mean that it reduces crime. It keeps criminals from committing more crimes while imprisoned [incapacitation], and also warns others away from committing crimes, or from spreading their drug habit to friends or family [deterrence].
AFF: But what if the most effective way to incapacitate drug offenders (and to frighten away future abusers) is to shoot stoners on sight?
NEG: But that's ridiculous.
The Neg could argue for some kind of "side constraint" on a utilitarian approach to punishment--that some punishments are just too awful--which might help the Aff show why a deontological approach is superior, because it rules out such punishments on principle, rather than ad hoc.
The Neg could also try to argue that society won't flourish with the population living in fear of summary execution--but will likely have no evidence, and, more important, no bright line for distinguishing more or less draconian punishments (and how they might affect society more broadly).
It's also quite possible that the Neg will swallow the bitter pill of consistency and try to defend a draconian approach as legitimate.
Regardless, the Affirmative has the Neg on the defensive, which is the point of CX.
That's all I have for now. In the comments, suggest questions (or lines of questions) that might work--or have worked for you.