Just a few facts
It's not the job of the police to protect you. Their role is to apprehend the criminal after the fact. Yes, there is some deterrent in their presence but as my father said, "Locks only keep honest people honest." The criminal pays no attention to locks - or police.
There's a very simple question that needs to be answered: Do you believe that an American Citizen has the right to defend their life, their property, and the lives of others anywhere they have a legal right to be?
But the first argument you get from the anti-gun believers is, "That's what the police do." The anti-gun crowd loves to cite statistics regardless of how skewed they may be but they'll never bring up the following.
Across America there are, on average, 2.4 sworn police officers for every 1000 citizens. In the cities, the lowest ratio is 1.1 and the highest - let me say that again - the HIGHEST is 4.4 per 1000. And that city with the highest ratio of 4.4 per 1000 population is Chicago, if you can believe it.
http://reason.com/blog/2013/09/17/chicago-tops-major-us-cities-with-44-swo
Divide that by three shifts and we see how well the police can protect any one person, family, school, church, theater, or gathering. Look up your city here:
https://www.fbi.gov/about-us/cjis/ucr/crime-in-the-u.s/2012/crime-in-the-u.s.-2012/tables/78tabledatadecpdf/table_78_full_time_law_enforcement_employees_by_state_by_city_2012.xls/view
The point is that the U.S. Constitution does NOT guarantee protection. It guarantees the RIGHT OF THE INDIVIDUAL to protect one's self, property, and others and that's what makes this very elegant question so very important. In the end, it is always up to the individual in the moment to protect themselves, their property, and others.
If government has any responsibility at all, it is to protect our right to protect ourselves, our property, and others.
I have rural property and I have a home in a large city. Living in a city removes one mostly from the danger of wild animals and makes people feel more secure. But the truth is that population densities in cities are very high which means people in cities are surround by the most lethal predator on the planet at all times - humans. That doesn't just apply to America.
The only thing worse than no security at all is a false sense of security.