I see the Death Squads as a legal division of the Police Department, an extreme extrapolation of assuming accused criminals to automatically be guilty and a drain on society. The Arch-Conservative logic in this is that the police have the rights to just kill you if you've broken the law, as the death penalty already applies to every crime in the book. They're the most extreme and immoral of all police types.
The way I see it, Police Negotiators are law enforcement who sympathize with suspects and want what's best for them, as is fitting in an Elite Liberal society. They don't want to hurt the suspects, they want to heal them of whatever caused them to resort to breaking the law in the first place, and so argue instead of carrying guns. If they weren't police, the LCS would probably mark them as Liberal.
Below that are the standard Police Officers, who are basically normal people trying to make sure the law is enforced to the letter. They don't particularly hate or sympathize with suspects, they just care about what is legal and what is not. If they weren't police, the LCS would probably mark them as Moderate.
Below that are the Police Gang Units. The name says it all, they're normal police that have fallen into a cynical and conservative view of the world and the lawbreakers in it, becoming like the very gangs they're trying to fight. The only real difference now is that this is a gang supported by the law of the land. They don't see criminals as real people with rights and feelings anymore, just lawbreakers to be punished. If the suspects get hurt along the way, who cares? They shouldn't have broken the law, those bastards. The LCS sees them as Conservative, and that's accurate even though they're police.
And below all of that is the Death Squad. A mobile and ever present death penalty for anyone who dares to break the law of the United States of America. They're everything bad about closed minded people and the law rolled up into one insane package and stamped with the national seal of approval. They would probably say things along the lines of: "Fuck the people, they're all just criminals waiting to happen! God would never tolerate such disobedience, and we won't either! Anyone who breaks the law hates America, and anyone who hates America deserves to die!" That's why I like the Death Squad as a game concept. There really are people who make statements like the ones I wrote, and the Death Squad are those people given a badge and a rifle. That is a goddamned scary thought. This also provides an interesting contrast to the Police Officers and Police Gang Units who are still around when the Death Squad is established. They may not be very good people, but at least they're still sane. The LCS sees the Death Squad as Arch-Conservative, and that's really accurate even though they're police.