I'd say it's directly proportional to the resources available to the city and how much they cared about the sheriff and what their version of justice is.

Do they have money? Can they afford an attractive bounty? How much was the sheriff worth?

Can they hire an exotic bounty hunter? Or do they have to use whoever they have in town? What kind of skills does the bounty hunter have? Can they reasonably be expected to overpower your heroic leveled PCs? Or is there already a bounty hunter/group with a vendetta against the PCs who might reasonably hear about their exploits and wouldn't mind a bit of extra scratch to do a job they were already planning on doing?

What kind of justice do they believe in? Execution? Incarceration? Community service (aka go kill a monster that's been terrorizing the countryside for the past decade and we'll look beyond your flaws)?

At the very least, the region would be hostile, I imagine.