I seem to recall that Ollie North composed an "extended list " during the Reagan administration. He had no authority to do so, of course. Does anyone else recall that incident?
Billdo, you are undoubtedly correct. And if Congress is in session or has been called into session, then no problem. But a problem arises when Congress has adjourned sine die without scheduling or providing for an adjourned session, in which case–in the absence of a President or an acting President who can call a special session under article I, § 3–Congress cannot reconvene until the following January, when it automatically convenes under amendment XX, § 2. Congress often adjourns in the late summer or early fall without another regular session scheduled until the new year. (Congress has usually adjourned in recent years pursuant to a joint resolution that lets the presiding officers call it back into session. But such a provision would not help if the presiding officers had fallen victim to whatever event exhausted the line of succession.) The decapitated government would then be operating for several months without a chief executive or a legislature, and with no lawful way of filling the presidential vacancy or reconvening Congress.
This situation nearly occurred during the Arthur administration. The Vice Presidency was vacant, Vice President Arthur having succeeded to the Presidency in 1881 after President Garfield’s assassination. The 47th Congress, and with it the tenure of the Speaker and the president pro tem, expired in March 1883. The 48th Congress did not convene until December, leaving a nine-month interval during which President Arthur served with no constitutional or statutory successor. (The Presidential Succession Act of 1792, then in force, provided only for the president pro tem and the Speaker–in that order–as statutory successors.) President Arthur dealt with the issue by secretly signing a proclamation convening Congress in special session, and sealing the proclamation to be opened only in case of his death or incapacity. As it turned out, the secret proclamation was never needed, but three years later Congress did enact a new Presidential Succession Act adding the cabinet officers to the line of succession (and removing the congressional presiding officers, who were added back in at President Truman’s recommendation in the 1947 Act, the one in force today).
Thanks, KenP! I didn’t recall the incident involving Colonel North, but his heyday would have roughly coincided with the article in The New Republic that I mentioned in the OP, so I ran a search that found several variations on the story that I recall.