Are the police obligated to protect citizens from harm?

On your Facebook page, you recently posted a story about a man who had to fight off a crazed knife-murderer in New York's subway, in full view of police officers, there specifically to capture this madman. Yet they did never interfered until after the knife-weilder was disarmed and on the ground--and the defender passed out with multiple stab wounds. Unsurprisingly, the man sued the NYPD. The suit was rejected, however, on the grounds that police are not obligated to protect people from harm. Indeed, the Supreme Court had decided just that question in a case in 2005 involving police failure to enforce a restricting order against a woman's estranged husband, resulting in the kidnapping and murder of their three young daughters. But did the Supreme Court decide correctly? I can see both sides here. On the one hand, how can any individual police officer have a duty to put their life at risk? On other hand, if the whole justification for government's existence is to protect individual citizens' rights, how can they not be obligated to protect their lives and limb against violence?