The president can't fire the employees directly but he can direct those under him to fire them. But then it has to be for cause. If what is alleged is true, it seems some of those people are eligible to be fired without cause.
And I suppose even if he can't fire them, he could re-assign them to storage room B. And take away their stapler. Probably shouldn't do the latter. Things could get heated.
What about moving their comfy little nest of vipers way out west into flyover country. Seems like in the first such move I read about 2/3 of them quit. That seems like a pretty good housecleaning and all nice and legal, too and I doubt it was the people really doing the work who would quit anyway. Probably bureaucrats who would go looking for some new nest of #resistance, so after the first move, institute a hiring freeze at the other agencies