In 1865, following the Night of Terror brought by the Booth Conspiracy Abraham Lincoln summoned the US Congress into session on this the first Monday after Easter.
Booth Conspiracy brings Night of Terror, Part 2 by Ed, Allen W. McDonnell & Jeff ProvineIn a solemn address he paid his dutiful respects to the two dead national leaders, Vice-President Andrew Johnson and Secretary of State William Seward. Also his gratitude to the military policeman who had intercepted John Wilkes Booth at the Ford Theatre.
Having reflected on the events of April 14th, and after holding several rounds of intense discussions with the Cabinet, Lincoln had developed a robust set of proposals that would safeguard the Federal Government from a re-occurrence of such a future conspiracy. Accordingly, he was asking for a Constitutional Amendment that would make the post of Vice President equal to those of the Cabinet, a person appointed by the President to serve at his pleasure as the President of the Senate (the official title of the Vice President).
The Amendment easily passes the joint session of Congress by the necessary margin and was also passed quickly by the States of the Union making it part of the Constitution. From the election of 1868 onward people only elect the President, the Vice President and Cabinet Secretaries are appointed by the President with the Advice and Consent of the Senate. However in his auto-biography, Lincoln would reveal that an even more far-reaching proposal that was considered - the President to also appoint a new position, President of the House  as a second Vice President.