There isn't really a good answer here because we're zoomed out so far and speaking hypothetically. The trick is to keep yourself laser focused on the now. This specific situation with this specific set of negotiated possibilities and that specific roll. Depending on the details, failure at desperate position could be immediate harm (the deserter loses his nut and stabs you) or a worsening overall situation, or any number of things really. It's all about specific context and the GM-player negotiation of action/consequence about that specific context.Is a desperate consequence then a fight starts (for example) or harm is done (the assumption is that a fight starts and the PCs get beat because they failed)? I guess what I am asking is how granular is it?
Again, just for comparison sake:
In D&D or Savage Worlds or whatever, the PCs would try a Persuasion roll and if they failed we would roll initiative. If it is not that, what is it in Band?
The a large extent though, generally speaking, the consequences flow from the specific goal of the stated action. So a 'talking' solution might produce very different consequences depending on whether the player was trying to get the Deserter to change his mind full stop, or accept a bribe, or even to try and drive a wedge between the deserter and his gang of thugs. The specifics are the key.