It seems that the Vice President has declared himself to be a fourth branch of government. Cheney's contention is that because the vice president has both executive and legislative duties (remember, he's the president of the Senate), neither of those branches can control him. It appears that the vice-presidency is not exactly the "warm bucket of spit" John Nance Garner thought.
But if neither the president nor the Congress can control him, what is to prevent Cheney from consuming the entire republic, like Godzilla on a bender? Rahm Emmanuel has taken the first step in solving this conundrum, by proposing to delete funding for the Office of the Vice President from the executive branch appropriations. That is a great step, but it is only the first step. I think what needs to happen is that the vice-presidency, at least for the remainder of the incumbent's term, needs to be allowed, nay, required, to flex its own execulegislative muscle.
Dick Cheney needs to pass his own appropriations bill to cover the expenses of his office. I am certain that David Addington can come up with a constitutional argument that would allow this; if not, he probably knows John Yoo's phone number. With his legislative power, he can deem his bill passed, and with his executive power, he can present his warrant to the secretary of the treasury. Then he can wait for a check.
If this were to happen, my suspicion is that Dead-Eye Dick would ultimately come to regret the lack of Mrs. Cheney's salary check as a U.S. Senator from Wyoming.