The Vice-President has never been called upon to cast a tie-breaking vote for any kind of presidential appointment — Judge, Cabinet Member, Ambassdor...nothing.
I suggest under the US Constitution he cannot.
Article I, Section 3, Clause 4 of the US Constitution states:
4: The Vice President of the United States shall be President of the Senate, but shall have no Vote, unless they be equally divided.
As we all know, Article I of the Constitution is about the Legislative Branch. So yes, clearly for legislative matters the Vice-President can cast a tie-breaking vote.
The Power of Presidential appointments is however not in Article I. That power is in Article II, Section 2, Clause 2 which states:
2: He shall have Power, by and with the Advice and Consent of the Senate, to make Treaties, provided two thirds of the Senators present concur; and he shall nominate, and by and with the Advice and Consent of the Senate, shall appoint Ambassadors, other public Ministers and Consuls, Judges of the supreme Court, and all other Officers of the United States, whose Appointments are not herein otherwise provided for, and which shall be established by Law
There is no precedent which indicates that “...with the Advice and Consent of the Senate” is meant to include the Senate AND the Vice-President if necessary. It has never happened.
I suggest that if a majority of the Senate cannot confirm someone that is it. Vice-Presidential tie-breaking is only for legislative business NOT Article II appointments.
Anyway, thought I would throw this out there and see if somehow I can be proven wrong or this matter can be brought to a Senators attention to make a point-of-order should the Vice President cast the tie-breaking vote.
Of course, litigation can always follow in the courts.
Update: Here is an interesting case about whether a Lieutenant Governor can cast a tie-breaking vote in a 20-20 evenly divided Kansas state senate on the question of a US Constitutional Amendment which must be approved by the Legislatures:
supreme.justia.com/…