I'm no expert but even I've read that "Works at the White House" is bigger than the executive residence and oval office, including the West Wing and the big office building that's directly connected to it by basement walkways. The National Security Council maintains 24-hour watch operations in the Situation Room (which is more a 'complex' than 'room'), while regional desk officers routinely work late evenings to overlap with morning business hours in Europe and Asia.

I asked Gemini if my recollection was correct and got: "The EOP network (managed by the EOP Office of Administration in coordination with Presidential Information Technology Community entities like the White House Communications Agency) operates as a single campus enterprise network. Its high-speed backbone links the West Wing, the EEOB, the East Wing, and nearby administrative facilities such as the New Executive Office Building (NEOB) on 17th Street."

So, definitely an issue that there's a device with some rogue malware installed but the total workforce across all shifts at the White House Complex is roughly between 2,500 and 4,000.