After Lyndon Johnson became President upon the death of President Kennedy, there was no Vice President from November 22, 1963 to January 20, 1965, when Hubert Humphrey was sworn in as Johnson's VP.
The US Constitution made a provision for this, though. According to the Constitution's "Line of Succession" guidelines, the Speaker of the House of Representatives becomes President of the United States if the Vice-President is unwilling or unable to do so.
John McCormick (Democrat, Mass.) was Speaker of the House from 1963 until Hubert Humphrey was sworn in, so he was the "technical Vice President" in that he would have become President had President Johnson died/resigned/incapacitated during that time. During the time he served as Johnson's 'next in line", he received Secret Service protection just like a Vice-President would, and later wrote an article about his experiences during this time for The Boston Globe