Well good, you do realize that the Vice President DOES have legislative and Executive powers? This does not help you, except in Bizarro world.
Why the hell does it matter that the Vice President happens to be the President of the Senate since that is largely a ceremonial function. If he has both legislative and Executive functions I am sure he would be so happy to head on down to Congress to explain to them his reasons for not complying with the Executive Order. Wait! I forget, he isn't just a legislative agency anymore then is just an executive agency and therefore the executive rules don't apply anymore then do the legislative rules. Oh my! I forgot about that one. So which body does King Cheney answer to? Is he a legislative agency who must respond to legislative subpoenas and testify before legislative committees. If Congress decides to give him an assignment will Mr. Cheney accept that assignment because he is a legislative officer or will he start pontificating about how he is an executive agency. I think Congress could solve this problem really easy and send the GAO over to his fucking office and demand to see the documents and say: AS A LEGISLATIVE AGENCY YOU WILL ALLOW THE GAO TO REVIEW YOUR CLASSIFICATION PROCEDURES. Of course Dicky will claim to be an Executive Agency then.