> I'd be really surprised if Congress can stop the President from firing employees. He is the head of the Executive branch.

The President is bound by law in that role, and most of thr federal civilian workforce is covered by civil service laws that govern hiring and firing, they are not at-will employees serving at the pleasure of the President? And those laws create a legal property interest which means that no one in government can fire them without due process, and that to do so is a violation of not only the statute itself but the 5th Amendment as well. This has been litigated fairly extensively, as one might expect given the size of the federal workforce and the inevitability of disputes over thr legitimacy of adverse workplace actions.