Frankly, they would be better off with vacant positions then staffed by a Obama leftover. Of course it would expose that most of these jobs aren't needed to begin with and should be eliminated rather then refilled.
The new president shouldn't have to fire any of these people, their contracts should end the day before the outgoing president leaves office. No exceptions.
But until then, all incoming republican presidents should do the firings on day one. It would help refill some of those spots, which I am sure demos drag their feet on so their guy says on longer. Note that incoming Democrats rarely if ever keep on a leftover republican. Even one like a mccain.