No. If he could, don't you think John Adams would have fired Thomas Jefferson, Jefferson would have fired Aaron Burr, or John Quincy Adams would have fired John C. Calhoun, tho Calhoun resigned his office earlier to accept a Senate seat. For that matter, if Andrew Johnson had been impeached, Presidents wouldn't be able to fire Cabinet members at all, as the primary charge was violating the Tenure of Office Act which required the President to get the approval of the Senate to fire executive branch members who required Senate approval to take office.
That's actually part of the reason why I wish he had been removed from office, not to mention severely weakening the Presidency. In the context of a separate executive branch and positions that require Senate approval, I think the Tenure of Office Act was a good idea. In terms of executive offices, what exactly separates one from being subject to Senatorial advice and consent versus not?
It's true that Myers v. United States (1926) was against the Tenure of Office Act, but that's largely a line of jurisprudence that has been rejected ever since. Two of the greatest Justices to ever serve on the Court were in dissent on that decision, Louis Brandeis and Oliver Wendell Holmes. Admittedly, one of worst was also in dissent (McReynolds), but broken clock and all that... I think the dissenters were far stronger than the majority in that case. Indeed, none in the majority are memorable as particularly good jurists.
