IANAL, but I don't think there is any particular law allowing the police to use deadly force -- they just have the same self-defense and defense-of-others exception to murder laws that everyone else has. Self defense doesn't apply to threats like Anwar al-Awlaki that aren't immediate, even if they're extreme and inevitable--I can't shoot a guy for preparing to blow up a bomb an hour from now.

It's not the government killing people, it's an individual cop, and if they do so unlawfully the criminal exposure is personal. (In practice, prosecutors are reluctant to actually go after cops in anything but an extreme case, but this isn't unique to police killings)