Grammars used to identify a category of the subjunctive used in questions as the Deliberative Subjunctive. As the name indicates, these were questions about which there was some doubt as to the answer. In other words, they were questions asked in a deliberative context, not always expecting an immediate answer, but assuming the need for deliberation. They could even be used as exclamations which did not expect any kind of answer at all. This category, however, is a false category of the subjunctive. It is a rhetorical category, determined not by grammar, but by context. There are two ways to explain how this is a false category. First: is deliberation confined to the subjunctive? The answer is simply and unequivocally, "No." I may ask, "What are they doing?" (Indicative Question) or "What could we do?" (Potential Question) or "What should we do?" (Jussive Question) and in every case I may be uncertain, I may be asking for deliberation, or I may, in fact, be just expressing my own confusion and not expect any sort of answer at all. Second, is there any form of deliberation that would require the subjunctive because the subjunctive added something not already accounted for elsewhere? Again, "No." Allen and Greenough say: "such questions [that is, jussive questions] when addressed by the speaker to himself, as if asking his own advice, become deliberative or, not infrequently, merely exclamatory" (443). But this is a function of address, not of grammar, and I can do the same in the indicative. Woodcock says: "These [subjunctive questions] are most conveniently classified according to whether the question is evoked by a second party, or whether it is spontaneous. Only in the latter case is the subjunctive truly 'deliberative.'" (172). But the matter of who evokes the question is contextual, not grammatical, and, again, I can spontaneously ask someone else indicative questions as well as subjunctive questions. In fact, even Woodcock recognizes: "In questions that are truly deliberative, the indicative is almost as common as the subjunctive." This is a clear indication that "deliberation" is not a syntactical category; it is a function of context and rhetoric, not grammar. The fact that these two eminent grammarians disagree about what makes a deliberative subjunctive different from a jussive subjunctive (is it addressed to self? is it spontaneous?) indicates that it is a phantom elephant and these grammarians have merely found different parts of it.
How, then, do we understand the subjunctive in questions? The simple answer is: Ask what kind of answer the speaker is seeking. If it is an order or expression of duty, the question is a jussive question. If the speaker is asking for an opinion about potential or possibility, then the question is a potential question. Here we repeat that part of the discussion of the independent uses of the subjunctive that applies to questions.
The jussive question makes a request about duty and you can tell it is a jussive question if the answer is a command: "What am I to do?" "Go away!" quid faciam? abi! = jussive question with imperative answer. The potential question makes a request regarding how the addressee feels about the potential or likelihood of an event: "What can I do?" "You could sit still." = quid faciam? potes tacere. = potential question with a potential subjunctive (or possum) in the answer. Note: only context tells you whether quid faciam is a potential question or a jussive question. You cannot ask an optative question. I don't know why, but it does not seem to happen. If you can say, "What am I to do?" asking for a command, you should be able to say something like "What do I really pray will happen to him?" asking for a prayer as an answer, "May he die miserably!" It is possible, of course, that the grammarians simply have not distinguished a optative question from a jussive question.