(including the resident, uh, President, himself) are the Presidential Cabinet members. The first four in line are the Secretaries of State, Treasury, and Defense, and then the Attorney General.
No one has seriously yet considered the possibility that no elected official may be able to assume the office of President of the United States. However, in the 19th century, six different Secretaries of State eventually became President, and only two members of Congress, so there are certainly precedents to give credence to that possibility.
Treasury Secretary Mnuchin is one of the Cabinet most closely associated with the President, and if the President and VP were forced to resign, one might expect Mnuchin to follow them.
A President Mattis is almost credible, because of all of Trump's Cabinet, Mattis (and Tillerson) have been the most independently expressive. Many people might be uneasy about a General becoming President, but in fact the WWII European commander-in-chief Dwight D. Eisenhower was one of the better Presidents of the 20th century.
We need not even consider Jefferson Beauregard Sessions. If the US has come to that pass, and there is still a government, we must remember what the Duke of York said about the imminent usurpation of Richard II's throne by York's nephew, the banished Duke of Hereford (in the Shakespeare play bearing that King's name): "Things past redress with me are now past care."
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