Do we have more manufacturing workers or government workers?

You are right, if you said government workers.

Terence P. Jeffrey reports for CNS News,

...in August 1989, the seasonally-adjusted employment numbers for government exceeded the employment numbers for manufacturing for the first time. That month, manufacturing employed 17,964,000 and government employed 17,989,000.

Manufacturing employment in the United States had peaked a decade before that in June 1979 at 19,553,000

From August 2015 to August 2016 seasonally-adjusted manufacturing employment declined by 37,000--dropping from 12,318,000 last August to 12,281,000 this August.

The 22,213,000 government employees in August, according to the BLS, included 2,790,000 federal employees, 5,120,000 state government employees, and 14,303,000 local government employees.

Read more here.