There's a problem with penal substitution. Biblical sacrifices do not represent human attempts to purchase forgiveness; instead, they offer a ritual means of acknowledging the costliness of sin and alienation from God.
We may not fix all the wrongs done by our fellow Muslims, Christians, Jews, Buddhists, or Hindus, but we have the power, and the responsibility, to be constantly improving ourselves and our communities.
America needs a period of atonement before rushing into the same mistakes we've been making globally and domestically. The Jewish tradition is useful in that it not only focuses on individual lives, but on collective responsibility.