Really at this point Rick should take his gang away from the jail. This negotiation BS is retarded. I'd of taken everyone and moved them into the crazy street with all the traps he discovered with his son and Michonne.
The jail sucks. It's obviously not secure in any way. In a gun battle you are just boxing yourself in. They go to where they met his old buddy and they'd have it made and a much more defensible area than a run down, broken down old prison. And yes, they apparently did run out of food, so there is always that.
And Rick couldn't really shoot the gov in the face because Daryll, the hillbilly you are talking about, brought a crossbow to a gun fight! He had a one-legged old man and guy with a crossbow.