The President appoints the Chairman of the Fed, but cannot remove him. Whether this is the case here I do not know.
The Chairman of the Fed is in office for so many years and if his time is up, the President can dump him and nominate someone else. He is not there forever. That is why it was so dumb when Greenspan’s time was up that Bush renewed him for another term.
The commission consists of five members who are appointed by the President with the advice and consent of the Senate. The terms of the commissioners are staggered and the basic length of each term is five years. No more than three of the commissioners may be members of the same political party. The statute does not provide for a chairman. Until 1950, the Chairman was elected annually. Following Reorganization Plan No. 10 of 1950 (see, Reorganization Act of 1949, 5 U.S.C. Secs. 901-913), the President designates the chairman. Pursuant to this Reorganization Plan, the chairman succeeded to most of the executive and administrative functions of the commission. The Act does not expressly give to the President the power to remove a commissioner. However, for the purposes of this case, we accept appellants’ assertions in their brief, that it is commonly understood that the President may remove a commissioner only for “inefficiency, neglect of duty or malfeasance in office.” While the SEC must transmit evidence of criminal misconduct to the Attorney General, there can be no doubt the SEC is authorized to institute civil actions in the federal district courts to enforce various security laws.
22
Several conclusions can be drawn from this brief overview. First, as the President has the power to choose the chairman of the SEC from its commissioners to serve an indefinite term, it follows that the chairman serves at the pleasure of the President.
http://bulk.resource.org/courts.gov/c/F2/855/855.F2d.677.86-2319.html
The bottom line is the President can fire the Chairman of the FEC but he can also remove any of the members for cause. Probably wouldn’t be smart but it can happen.