@Dominions SonMadison is not the only one.
An officer of the United States is a functionary of the executive or judicial branches of the federal government of the United States to whom is delegated some part of the country's sovereign power.
US Constitution, Art II, ยง2, 2;
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 Department
Bush DoJ agreed (2007):
a position to which is delegated by legal authority a portion of the sovereign power of the federal government and that is 'continuing' in a federal office subject to the Constitution's Appointment Clause. A person who would hold such a position must be properly made an 'officer of the United States' by being appointed pursuant to the procedures specified in the Appointments Clause
DOJ Analysis
Detailed analysis from a different perspective (but supports my conclusion)
See this article for an interesting examination of the question of if the President is an 'Officer of the United States'
Per law professor Will Baude:
But the Speaker is not an "Officer of the United States." The Speaker is elected by the people, and Article II, Sections 2 and 3, says that "Officers of the United States" are to be appointed and commissioned by the President. So if "Officer" and "Officer of the United States" are the same thing, the presidential succession statute is unconstitutional (an argument made by James Madison, and later by Professors Vikram and Akhil Amar). But if Professor Tillman is right, i.e., if "Officer" and "Officer of the United States" are different, the statute is fine. And if the dispute is unresolved, it is a recipe for constitutional crisis.
Source: Bode
This is not a new controversy, Congress got it wrong in 1792 and has ever since. It's not just my opinion and others agree with Madison's analysis.