Glenn Reynolds of Instapundit graces the NYT op-ed page today with a short piece on the nature of the vice presidency.
Article I of the Constitution, which describes the authority of the legislative branch, says that "the vice president of the United States shall be president of the Senate, but shall have no vote, unless they be equally divided." Aside from the job of replacing a president who dies or is unable to serve, the only vice presidential duties that are spelled out in the Constitution are legislative in character.
But if the vice president is a legislative official, then the exercise of executive power by the vice president raises important constitutional questions related to the separation of powers. The Supreme Court has held on more than one occasion that legislative officials cannot exercise executive power. The Court would likely dub this a "political question" that is beyond its purview, but Congress is empowered to remedy this sort of thing by legislation.
And Congress should do just that: pass a law to prohibit the vice president from exercising executive power. Extensive vice presidential involvement in the executive branch — the role enjoyed by Dick Cheney and Al Gore — is not only unconstitutional, but also a bad idea.
For Reynolds' extended analysis of the vice presidency (and an answer to the question "Is Dick Cheney Unconstitutional?"), see this paper on SSRN.