No, it is not necessary for normative principles to bear reference to God to produce a feeling of obligation in a moral agent. While religious traditions often link moral obligations to divine commands or rewards/punishments (Divine Command Theory), secular ethical frameworks demonstrate robust alternative grounds for moral obligation.

Justification:

1. Rational Autonomy (Kantian Deontology): Immanuel Kant argued that moral obligation stems from human reason itself. Rational agents recognize universal moral laws (categorical imperatives) that they impose upon themselves. The feeling of duty arises from respecting this rational law, not divine command. For example, the duty not to lie is derived from the impossibility of universalizing a maxim of lying.

2. Consequentialism (Utilitarianism): Philosophers like J.S. Mill argue that actions are morally obligatory if they produce the greatest good for the greatest number. The feeling of obligation arises from the recognition of positive societal outcomes and empathy, independent of divine decree.

3. Social Contract Theory: Thinkers like Hobbes and Locke suggest that moral duties arise from rational agreements (explicit or implicit) necessary for peaceful societal coexistence. Obligations are undertaken out of mutual self-interest and a desire for social order.

4. Virtue Ethics: Here, obligation stems from the desire to cultivate a good character (virtues) and live a flourishing life (eudaimonia), guided by practical wisdom, rather than obeying external rules, divine or otherwise.

In practice, millions of atheists, agnostics, and individuals from diverse philosophical backgrounds experience profound moral obligations without reference to God. Their sense of right and wrong, and their commitment to justice, empathy, or societal well-being, are rooted in shared human rationality, emotional capacity, and social structures. While belief in God can certainly reinforce moral motivation for some, it is demonstrably not a necessary precondition for the feeling of moral obligation itself.