An important data point on employment number conspiracy theories

Just heard on the radio that there are 157,000,000 people working in the United States. That means that, if the jobless numbers are off by 0.1%, they’re off by 157,000 workers.

Never say never, but  assuming the current batch of numbers is off by half a percentage point, its hard to fathom how publicly-available job numbers can be cooked up in such a way that nobody notices 7 to 8 hundred thousand uncounted workers? And I think we can agree: half a percentage point is the bare minimum you’d need in order to make cooking the books worth the effort in this case?