Physical Danger
In day-to-day life, being a small town mayor or councilor is no more dangerous than your typical office desk job; in fact, it may even be safer. Whenever you make any high-profile public appearances, there'll usually be a police detail somewhere nearby. If you're driving to an event, you just have to say the word and an escort will get you there safely. The only heavy lifting you're liable to do is when you've got to use those massive scissors they give you during ribbon-cutting ceremonies.
Of course, America's history is filled with examples of people who decided to take their anger out on people in government. As long as humans can disagree about something, some will take their disagreements to an extreme level.
There are always going to be people who'll see your power as a threat to them in some way. It could be a lifetime criminal, your neighborhood anti-government conspiracy theorist, or even just a concerned citizen who is mad as bees about the new zoning regulations and isn't going to take it anymore. But this is the exception, not the rule.
One big difference here are those sheriffs who also have to run for office. If you're the locally-elected sheriff, your job is a danger-hybrid of political desk job and law enforcement officer. You're still going to mostly be behind a desk, it just happens to have a gun in one of its drawers.