I've been telling reporters who ask about executive privilege that if Congress and the President ultimately strike a deal about the conditions under which Karl Rove, Harriet Miers and/or others testify about the Gonzales Eight Massacre, the terms of the deal will likely reflect the parties' relative bargaining power, which in turn will depend on how the issue is playing with the public. The latest Pew poll shows that most people aren't paying much attention to the story. To my mind, such inattention favors the administration. If people think that the scandal is much ado about nothing very much, they're unlikely to regard efforts by Congress to get to the bottom of the story as especially important.
To be sure, public apathy could cut the other way: If people think the issue is no big deal, they might think the administration is overreacting by not just revealing everything there is to know about it. But I think that's unlikely. I would expect that the "prosecuting" side of an investigation benefits from public interest. This may be why Whitewater --- which almost nobody ever understood and therefore which almost nobody cared about --- lacked legs as a scandal, while the Lewinsky Affair, with its prurient appeal, played well for a Republican Congress. Conversely here, absent some salacioius revelation, apathy favors the administration.
In any event, even if we judge the public yawn as a wash, Bush's own commitment to executive privilege as a matter of ideology may be enough to ensure a genuine stalemate. My fellow FindLaw columnist John Dean has an interesting analysis of that aspect of the issue here.