executive privilege

"WASHINGTON, July 9 — President Bush invoked a broad interpretation of executive privilege on Monday in his confrontation with Congress over the dismissal of federal prosecutors, refusing to comply with subpoenas for documents and blocking testimony from former White House aides."

I really want to understand the logic...

If Vice President Dick Cheney is, in fact, a member of the Legislative Branch of government as he claims and not the executive branch - can Senator Patrick J. Leahy of Vermont rightfully subpoena him to testify because he does not fall under executive privilege?

All this President needs is a bulbous red nose and some big red shoes.