I am currently reading through the Compendium of the Social Doctrine of the Church and I thought these paragraphs quite appropriate concerning the HHS mandate.
398. Authority must enact just laws, that is, laws that correspond to the dignity of the human person and to what is required by right reason. “Human law is law insofar as it corresponds to right reason and therefore is derived from the eternal law. When, however, a law is contrary to reason, it is called an unjust law; in such a case it ceases to be law and becomes instead an act of violence”. Authority that governs according to reason places citizens in a relationship not so much of subjection to another person as of obedience to the moral order and, therefore, to God himself who is its ultimate source. Whoever refuses to obey an authority that is acting in accordance with the moral order “resists what God has appointed” (Rom 13:2). Analogously, whenever public authority — which has its foundation in human nature and belongs to the order pre-ordained by God  — fails to seek the common good, it abandons its proper purpose and so delegitimizes itself.
c. The right to conscientious objection
399. Citizens are not obligated in conscience to follow the prescriptions of civil authorities if their precepts are contrary to the demands of the moral order, to the fundamental rights of persons or to the teachings of the Gospel. Unjust laws pose dramatic problems of conscience for morally upright people: when they are called to cooperate in morally evil acts they must refuse. Besides being a moral duty, such a refusal is also a basic human right which, precisely as such, civil law itself is obliged to recognize and protect. “Those who have recourse to conscientious objection must be protected not only from legal penalties but also from any negative effects on the legal, disciplinary, financial and professional plane”.
It is a grave duty of conscience not to cooperate, not even formally, in practices which, although permitted by civil legislation, are contrary to the Law of God. Such cooperation in fact can never be justified, not by invoking respect for the freedom of others nor by appealing to the fact that it is foreseen and required by civil law. No one can escape the moral responsibility for actions taken, and all will be judged by God himself based on this responsibility (cf. Rom 2:6; 14:12).