I spoke to Nash (in Primm) about needing a new sherrif after cleaning the hotel and then went to Meyers and spoke to him about being sherrif.
He means doing it after helping NCR take back the prison. It would be nice if the dialog post-recapture emphasized this but part of the reason he even had a chance to be pardoned to be sherif was because he was effectively already free. I think one of the dialog options you get for convincing them to pardon him was something to the effect of "How is this worse than what's going on now."
Once they retake the prison the immediate threat to the town of primm is reduced (assuming you cleared out the bison which you have to do first anyways) and they also have those troops they had been using to hold back the powder gangers suddenly free to do the authoritarian occupation style of policing that they do in much of the mojave.
Really- Primm Slimm is your best choice in terms of being a "good" sheriff. I mean the convict's inaugural speach was really just a him threatening to shoot people. So what if the robot forgot the name of the town in his speach... and can be hacked by Vicki and Vance impersonators... sadly he's still the best option.
Anyways Lee tells you to talk to Hayes after you have secured the prison and killed the leaders- by then he has already started trecking out towards the middle of rad-scorpian infested nowhere (maybe forlorn hope) and you'll be lucky to catch him or even find his body if you're not quick.
But yeah in the same completion of that sequence of quests I have the radio announcer playing the "you failed" track and the wandering idiot lieutenant saying how obvious it was we succeeded. Maybe Primm and the nearby prison are going to be our reminder of Gecko/Vault City in that sense- doing all the things for one particular resolution but having the game partly acting as though they were not done. Hopefully the ending slides are right at least, but hey at least there are ending slides.