Only, an obsession against police brutality (which I don't really have... see below) leads to voting Republican??? Nahhh, most Republicans fail to see that the entire criminal justice system (along with the war machine) is just another example of the failure of government. That is mainly becaue they have a knee jerk reaction in defense, because the harm mainly falls on the poor and minorities and so they associate it with the left. Libertarians hate government because it hurts individuals, regardles of race, creed or class.
As I have explained before, I have just been plugging away on the police brutality because of Balko (one of the best bloggers/journalist alive) and I think there might be more of a niche there for libertarian ideas. You abuse the idea of the statist criminal justice system and the offensive military and there really is no good argument for government left.