And Schlesinger may provide an answer to a question I asked here. No one has ever seen much opportunity in President of the Senate.
Is the Vice Presidency Necessary? - The Atlantic (May 1974):
"It is a doomed office. No President and Vice President have trusted each other since Jackson and Van Buren. Mistrust is inherent in the relationship. The Vice President has only one serious thing to do: that is, to wait around for the President to die. This is hardly the basis for cordial and enduring friendships. Presidents see Vice Presidents as death's-heads at the feast, intolerable reminders of their own mortality. Vice Presidents, when they are men of ambition, suffer, consciously or unconsciously, the obverse emotion. Elbridge Gerry spoke with concern in the Constitutional Convention of the 'close intimacy that must subsist between the President & vice-president.' Gouverneur Morris commented acidly, 'The vice president then will be the first heir apparent that ever loved his father.'
At the Constitutional Convention, Roger Sherman noted that if the Vice President did not preside over the Senate, 'he would be without employment.' Sherman's observation was prophetic, except that the Vice President's constitutional employment is a farce. Mr. Agnew as Vice President, for example, never went near the Senate if he could help it. Early Vice Presidents of a philosophical bent filled their days by writing attacks on the power of the national government. Jefferson wrote the Kentucky Resolution as Vice President, Calhoun the South"