This gets sticky for a couple of reasons. First, of course, is the matter of oversight and separation of powers within the federal government. When one branch of government declares itself above the law and free from meddlesome oversight by other governmental branches, as required by the Constitution, what remains is the absolute annihilation of the rule of law and the end of America's form of government as it has been practiced for the last quarter of a millennium.
This specific issue is all but certain to wind up in the hands of the Supreme Court one of these days. The Congressional committees, whose subpoenas were spurned, decided to hold the White House in contempt, which initiated a legal process whereby the matter of Bush's definition of executive privilege will eventually be decided in the courts ... which brings us to Scary Problem #2.
There is no settled, definitive, black-letter law on the books in America that specifically sets the parameters for the execution of and limitations on executive powers. The United States Constitution contains exactly 15 words in a single sentence explaining the matter, right at the beginning of Article II: "The executive Power shall be vested in a President of the United States of America." The Federalist Papers go in to far greater detail, but those are documents with no legally binding power, so this one sentence is really all there is.
Really interesting reading, and something to think about.