National Emergency Selective Service Act - Deauthorizes the Military Selective Service Act (requiring registration under the Selective Service System [System] for possible military induction) except during a period of national emergency declared by the President.

Provides for the suspension of local military selection boards, appeal boards, and other selective service system agencies and activities during non-emergency periods. Requires the Secretary of Defense (DOD), when System operations are suspended, to assume responsibility for the security of System databases.

Suspends sanctions against persons failing to register under the System, unless such failure occurs during a national emergency.

Permits the authorization of appropriations under the Military Selective Service Act only during periods of national emergency.