That is true. And when the president submits his/her budget to Congress, he/she can specify the staffing level they would like to have in each department.
Here is where it gets tricky, though. If the president requests a lower staffing level than currently exists and Congress appropriates budget for that staffing level, then the president can eliminate (lay off) the positions that were not funded. But if Congress ignores the president's budget request and funds all existing positions, it is almost impossible for the president to lay off or fire anyone to get down to the level he/she thinks is needed. The only option then is attrition - not replacing those who retire or quit.
Which is why Fiorina's statement is gutless. I'd like to see the courts try to specify how many people I need to "protect" the desert tortoise.