This is almost too easy. Here's how it's going to go down.
Congress has issued subpoenas. The White House has refused citing executive privilege. The fight will end up in the Supreme Court, which will side with the White House on the grounds that this is not a criminal investigation. (It doesn't really matter. If it were a criminal investigation they would find some other excuse, but this is the most defensible argument for not following the Watergate precedent, so that is the one they will use.)
At that point, Congress's only option to restore separation of powers will be to impeach Bush, Cheney, and at least some of the members of the Supreme Court. Which they could do. But which, of course, they will not do because the Dems are spineless cowards who are afraid of their own shadows.
At that point American Democracy will be well and truly fucked.
Have a nice day.