By "on the job," I assume you mean actually performing the primary mission. Most federal agencies have about 15% of their work force actually engaged in performing the primary mission. The remaining 85% are overhead positions; unless you plan on not paying the people actually on watch, administering their personnel records, planning and monitoring budgets, maintaining facilities and equipment, responding to CONGRINTs, and processing the absolutely astonishing volume of paperwork associated with all those tasks, you've got to have those people.
However, there is a catch. That 15% figure is for those agencies that do not require 24/7 manning.
Bottom line: for each post, you have five bodies in rotation. Just manning one additional post per mile of the Mexican border with one person requires 10,000 persons.
Second, understand that for every person performing the actual mission, there's going to be about 5 people doing other work that supports accomplishing the mission, and those people are going to cost you $120K per body. TANSTAAFL. Now, maybe you're thinking of outsourcing that work to India to save money, but I don't think that's a wise idea.
Name the ones that are on watch 24/7, 365 days a year. Would that be the U.S. Postal Service?
No.
The U.S.P.S. has hired 750,000 workers for every 25,000 it has "on post" at any given time?
Does the post office deliver mail around the clock, 7 days a week, 365 days a year?
No, it doesn't.
Are you only planning to man the border on an 8/5 basis and hope that the smugglers take weekends and evenings off?
The U.S.P.S has hundreds and hundreds of 24 hr facilities. The U.S. Mail is continuously on the move from distribution center to distribution center.
Using your numbers, the whole country would have to work for the U.S.P.S..
LOL!