I can't speak for law enforcement, but I have a feeling that when things go bad, their primary mission is not what everyone is hoping it might be. When I was in the Marine Corps, I was assigned to the US Embassies in Yaounde Cameroon and Jakarta Indonesia. In both places, most people who worked at the Embassy, and US citizens who worked in those countries that I met, all felt that if things went bad, they would come to the embassy because the Marines would protect them. Unfortunately, our primary mission was to protect the classified material inside the embassy, and to keep everyone out of the embassy that was not authorized to be in there. It was the local governments responsibility to protect the people who worked at the embassy. Non embassy employees where pretty much screwed. There where five Marines in Cameroon, ten in Indonesia. We where armed with pistols, shotguns and uzi's, plus tear gas grenades. In every drill that we performed, the goal was to destroy certain things like encryption devices and documents before losing control of the embassy. This is what happened in Benghazi to some extent, except they had mercenaries instead of Marines protecting the Consulate.
I think that we have seen that during a natural disaster and during riots, the police are concentrated at certain government buildings. They do not go out to protect the people, they do not go out in small groups to patrol or do anything until it's safe for them to do so. During Katrina, I believe the majority of them waited until the National Guard arrived before they where able to start enforcing the law. During the riots in Baltimore, the police where told to let the rioters do what they wanted and to not interfere. People died and property was destroyed because of political decisions made by the mayor.
To rely on the police, or even expect help from them is hopeless until order is restored. How long that takes will depend on the situation.
