Obviously, if there's misfeasance/malfeasance you can sue. If LE was 10 seconds too late and did everything properly; that's part of the world we live in.
I don't know if you have read the case law that shows there is no duty to protect, but it is a bit more than 10 seconds, and is up to and including never responding.
In the Warren case two roomates upstairs heard their third roomate downstairs being attacked by intruders. They called the police.
This was in DC where gun laws at the time were very strict (no handguns could be purchased), and the law required all firearms including rifles and shotguns be kept "unloaded and disassembled or bound by a trigger lock."
It continued for awhile, and they called the police again, who once again answered and dispatch alerted local police.
The third woman downstairs finally stopped screaming after about 30 minutes.
The two women assumed the police they had called twice had finally arrived and stopped the attackers.
They called down to their roommate which alerted the intruders.
The intruders, two men, then took all three of the women and proceeded to beat and repeatedly rape them for over 14 hours.
Police were found by the Supreme Court to not be liable in any way whatsoever.
"fundamental principle of American law that a government and its agents are under no general duty to provide public services, such as police protection, to any individual citizen."
You can call 24 times over 24 hours and they can never respond and still not be liable.
The only people the government and its agents are held liable to protect are those in their custody. Prisoners, arrested or restrained individuals, or others who are in the care of the government against their will.
That said I have heard of states with a law requiring someone to report a crime or assist.
I know California has such a law passed in 1999 if you witness a crime on a child under 14 years old (read about it in a gang rape case last year of a 15 year old where 4-5 individuals raped her and around 10 witnesses failed to report the incident and were not liable of any legal wrongdoing.)
So technically you could be breaking the law in California if you witness a parent give a harsh spanking/beating to a child and do not report it to police.
As noted by someone else, police must be assisted in some jurisidictins or instances.
They can also give a command to help them perform an arrest or detention, with penalties for failure to do so in some locations.
They can even take personal property of others to assist them against the will of the property owner on occasion.
They can in fact commandeer vehicles, like common in some movies during police chases.
(Though the individual would be entitled to reimbursement for damages. But blue book values are often less than the real value of the vehicle, or something similar you could replace it with. If a vehicle in excellent shape with excellent maintenance, with the engine just completely redone was totaled, they may only be entitled to give you the used blue book value of an X year old car.)
