You can use hyperbole and point to an occasional extreme example all you want, but the fact is that he is absolutely right. All the sheriff did here was state the facts. He didn't tell everyone to arm up and roam the streets, he simply stated that you are your first line of defense. People wanting to make political hay have (unsurprisingly) jumped into the mix here. There are your typical politicians and gun control groups saying what they typically say. In actuality, what they are saying is quite dangerous. Law enforcement is rarely ever there in time. Stating that he should "do his job better" makes no sense statistically. A fantastic law enforcement response time is around 2 minutes. The averave, or "acceptable", is probably more in the range of 4 to 5 minutes. Add at least another 5 minutes if you live in a rural area. A sheriff generally has a much wider area that they have to police. It just takes time to drive somewhere.
So, let's take a very good response time of 2 minutes. Look at your watch. Someone has just kicked in your door. Sit there and watch 2 minutes go by and tell me if that isn't an eternity. Now, response time on scene, not actually involved in your crisis yet. So, the police pull up and need to assess the situation before charging in. Add on another minute at least. Now you're in your bedroom with the house surrounded by the police and the bad guy trapped inside. Now what? What is actually irresponsible is telling citizens that they should rely on law enforcement response as their primary means of defense. Calling 911 should be the same as an officer callingfor back-up. That is how everyone should view that system. Find a good defensive place, get the family there and hold your position, ready to use your firearm, while waiting for back-up to arrive. No "Dirty Harry" about it, just a family defending their lives and home.