Final answer:
The main duty of the U.S. Vice President is to preside over the Senate and cast tie-breaking votes. The constitutionally defined role is limited, but the actual influence of the Vice President varies depending on the administration's use of the office.
Step-by-step explanation:
The main duty of the Vice President of the U.S. is to preside over the Senate. This role includes casting tie-breaking votes when the Senate is deadlocked on a bill or a nomination. The Vice President's constitutional duties are minimal, and they essentially serve as a backup to the President, ready to assume the presidency if the President is unable to serve for any reason. Over time, the role of the Vice President has evolved, with some Vice Presidents taking on more ceremonial roles, while others have been actively involved in governance and have held significant influence within the administration.