Has natural law ever been asked of U.S. Supreme Court nominee in a confirmation hearing?
Whether or not a candidate for the U.S. Supreme Court believes there is natural law or what his thoughts of its role in human law are would pertain to his judicial philosophy, so it seems such a question would be asked of him.
Cicero De Republica 3.22.33 defines natural law (quoted in Integralism: A Manual of Poilitical Philosophy ch. 7 "Law" by Crean, O.P., & Fimister):
There is a true law, a right reason, conformable to nature, universal, unchangeable, eternal, whose commands urge us to duty, and whose prohibitions restrain us from evil. Whether it enjoins or forbids, the good respect its injunctions, and the wicked treat them with indifference. This law cannot be contradicted by any other law, and is not liable either to derogation or abrogation. Neither the senate nor the people can give us any dispensation for not obeying this universal law of justice. It needs no other expositor and interpreter than our own conscience. It is not one thing at Rome and another at Athens; one thing today and another tomorrow; but in all times and nations this universal law must forever reign, eternal and imperishable. It is the sovereign master and emperor of all beings. God himself is its author, its promulgator, its enforcer. He who obeys it not, flies from himself, and does violence to the very nature of man. For his crime he must endure the severest penalties hereafter, even if he avoid the usual misfortunes of the present life.