actually the president can fire any cabinet officer or (almost) any non-judicial appointment at any time. The Supreme Court has agreed that the president has this authority.
Hm, yes, I see on reading about the Myers v. United States decision that, as usual, Supreme Court jurisprudence makes less sense than it ought to. :-)
I still think, though, that a JCS Chairman in the position I described would question (and would be right to question) a President who conveniently fired a SecDef who did not concur with a nuclear launch order.
The rest of your comment is fine, but actually the president can fire any cabinet officer or (almost) any non-judicial appointment at any time. The Supreme Court has agreed that the president has this authority.
Granted, the appointment must be confirmed by the Senate in the first place, but the Senate does not hold a veto on the president removing any of these appointees after confirmation. The impeachment and trial of President Andrew Johnson was based on Congress' attempt to keep him from firing appointees, and that law was later ruled unconstitutional.