Final answer:
The nurse should first administer the ordered oral calcium supplement to a patient showing signs of hypocalcemia following a parathyroidectomy.
Step-by-step explanation:
The question involves a patient experiencing carpopedal spasms and tingling of the lips following a parathyroidectomy. These symptoms are indicative of hypocalcemia, which can occur post-parathyroidectomy due to a drop in parathyroid hormone levels, leading to decreased blood calcium levels. The first action the nurse should take is to administer the ordered oral calcium supplement to quickly address the low calcium levels and prevent further complications. Administering oxygen, using a muscle relaxant, or having the patient rebreathe from a paper bag are not initial priorities for these specific symptoms arising from hypocalcemia.