"Temporarily" hiring and firing his own employees is explicitly his Constitutionally defined job. Thats the actual purpose of the Executive branch, and as Chief Executive Officer of the United States that authority starts with the President.

The crazy part here is its never come up. Congress gets a say on hiring because they are the ones that approve budget increase requests. They don't get a say on budget decreases because there is no legal mandate to spend too much. The Courts don't either, because there is no law giving executive branch powers to other branches.