Nuclear Family Priority Act This bill imposes limits on various types of family-sponsored immigration visas. The alien parents of U.S. citizens shall not qualify for visas for "immediate relatives," which are not subject to any direct numerical limits. Currently, the spouses, unmarried children under 21, and parents of citizens are considered immediate relatives. The bill also creates a nonimmigrant visa for such parents of citizens. Such aliens shall not be eligible for employment or any public benefits. The bill also reduces the baseline annual cap for family-sponsored visas from 480,000 to 88,000, and revises the methods for calculating the cap. Preference allocations (visa categories subject to various annual caps) for various family-sponsored visas shall be eliminated, including those for the siblings and married children of citizens. The bill provides for a preference allocation for the unmarried children under 21 and spouses of permanent alien residents, subject to the 88,000 annual cap.