Let's assume that I am elected Vice President of the United States and am an evil, diabolical man. I behave badly, even criminally, in office. The House of Representatives impeaches me. I solemnly march into the Senate chamber for my trial. My team of lawyers takes its place in the designated spot on the floor. And I pick up the gavel and assume my post as the presiding officer at my own impeachment trial.

Under Article I, section 3 of the Constitution, the Vice President of the United States is president of the Senate. The same section of Article I specifies that the senate "shall have the sole power to try all impeachments." Thus, the Vice President of the United States is the presiding officer at his own impeachment trial. Q.E.D.

There's no way around this one. Nowhere does the Constitution say that the Vice President is stripped of his power as presiding officer of the Senate just because the business at hand is his own impeachment trial. The president pro tem clause specifies that that officer serves "in the absence of the vice-president or when he shall exercise the office of president of the United States." The Vice President is not "absent" when he's before the Senate for his impeachment trial, and he certainly is not exercising the office of President of the United States.

The power of each house of Congress to make its own rules of proceedings cannot be used to strip the Vice President of his specific constitutional prerogative -- one of the few he has -- as president of the Senate, or to accomplish the same thing by deeming the Vice President "absent" if he is impeached. Unlike the House, which has unrestricted power to choose its Speaker and other officers (and thus can strip the Speaker of his powers if it likes), the Senate is stuck with the Vice President. Its rules-of-proceedings power is bounded by the fact that the Vice President of the United States must remain the presiding officer of the Senate.

It follows that the Senate may not, consistent with the "President of the Senate" clause, effectively deprive its president of the power to preside by making his rulings impotent or by vesting a superior power to preside in some other officer, or in a committee, or in the body as a whole. …