No.
Once a nominee is confirmed by the U.S. Senate, that approval is final and may not be withdrawn or revoked, as a consequence of the United States Constitution. At that point, the only power the U.S. Senate has over the appointee is to impeach that individual, or to abolish the post to which that individual was appointed entirely by law. No law passed by Congress and no Congressional rule can change this fact.
This is a point so completely settled and obvious that I do not believe that it has ever been litigated. Certainly, the U.S. Senate has never purported to withdraw or revoke its confirmation of a nominee.
Congressmen delegate their power of advice when they nominate
department heads.
This is a fundamental misunderstanding of the advice and consent power of Article II, Section 2, Clause 2 of the U.S. Constitution, which in the course of enumerating powers of the President states:
He shall have power, by and with the advice and consent of the Senate,
to make treaties, provided two thirds of the Senators present concur;
and he shall nominate, and by and with the advice and consent of the
Senate, shall appoint ambassadors, other public ministers and consuls,
judges of the Supreme Court, and all other officers of the United
States, whose appointments are not herein otherwise provided for, and
which shall be established by law: but the Congress may by law vest
the appointment of such inferior officers, as they think proper, in
the President alone, in the courts of law, or in the heads of
departments.
It is not a power of Congress, in general, it is particular to the U.S. Senate.
The U.S. Senate can provide advice and consent to the President, directly, regarding who should be appointed to certain positions requiring U.S. Senate approval (there has been some debate over whether that advice should be pre-nomination or post-nomination, but there is no debate that it must be pre-confirmation), and regarding treaties.
The advice and consent power is not global as to all actions of the President; it applies only to treaties and appointments. And, it is never delegated. Consent to an appointment is consent to the momentary act of hiring someone for a position. Once that act is completed, there is nothing to withdraw consent to that is not a fait accompli, the appointment has happened. The U.S. Senate consents only to the act of hiring someone and not to the continued employment of someone.
Conceptually, hiring and firing personnel in the executive branch is an executive branch function. The U.S. Constitution's appointments clause, which is in Article II of the U.S. Constitution pertaining to the Presidency, contains a small check on the President's power to hire executive branch officials by requiring U.S. Senate approval for the President to appoint certain senior executive branch officials determined by law. Once that narrow check on the President's power is overcome, the default principle that personnel matters in the executive branch are the President's problem and not for Congress to have a say in, in the strong President form of government that exists in the United States, is restored.
This is an application of the principle of separation of powers with checks and balances, as set forth by James Madison in Federal Paper No. 51 (which is authoritative because the Federalist papers are legislative history for the U.S. Constitution and represent the intended meaning of the document which was considered and effectively adopted by ratifying states when the U.S. Constitution was presented for ratification. The Federalist papers are basically the contemporaneous official commentary to the U.S. Constitution, written by its proponents, which elucidate its meaning, given the brevity of the U.S. Constitution. Federalist Papers 65-67 (written by Alexander Hamilton) also clarify the contemplated meaning of Article II, Section 2, Clause 2 of the United States Constitution and how that interacts with the impeachment power.
Because the U.S. is not a parliamentary system of government, Congress does not have a say over the day to day operational decisions involved in running the government, such as monitoring the performance of senior government officials once they have been appointed and firing them if they fail to perform.
