The niggling detail that Mr Bush and his White House staff have so far been unable to swat away is Valerie Plame, the CIA agent whose cover was blown after her husband, a former diplomat, displeased the President. Ms Plame has remained silent. Her husband, Joseph Wilson, however, has made no secret of his belief that his wife's identity was deliberately leaked by the White House in a petty act of revenge.
Mr Bush's difficulties stem from three awkward facts. The first is that knowingly to reveal the identity of an undercover agent is a crime in US federal law. The second is that the answer to the standard question - who benefits? - would strongly implicate the White House. And the third is that the man the investigation is closing in on is Mr Bush's closest adviser, Karl Rove, the tactical genius to whom he owes his re-election.
As with previous second-term presidents, the actual episode that gave rise to Mr Bush's current discomfiture took place towards the end of the first term. And it is legitimate to ask whether, had America known then even the skeletal details it knows now, Mr Bush's re-election would have been so smooth. Indeed, there must be a strong suspicion that Mr Bush approved the appointment of a special prosecutor in the hope of delaying the emergence of any unpalatable revelations. Special prosecutors have a habit of taking their time.
But precedent shows that, once appointed, they take their responsibilities seriously. And Patrick Fitzgerald is no exception. He has already elicited an admission from Karl Rove's lawyer that Mr Rove confirmed Ms Plame's identity to a reporter. Two journalists have given information and a third is serving a four-month prison term for refusing. Most damaging of all, Mr Bush, through his spokesman, has been forced first to retreat into embarrassed silence and then to back-track. Having initially said that the leaker would have no place in his White House, he now says that anyone found to have committed a crime will be removed. However much his spokesman insists otherwise, this is not the same thing.
The Bush White House is now in full defensive mode, setting up tank traps and decoys all over its lawns. A large part, but not all, of the US journalism establishment is up in arms about a reporter's obligation to defend the confidentiality of his or her sources, and the (Republican-majority) Senate is discussing whether to make withholding the identity of a source into a journalist's statutory right. Memos and e-mails are surfacing all over Washington that have at most a peripheral bearing on this case, but are widely disseminated.
All this looks suspiciously like obfuscation. What is required here is a simple answer to an equally simple question: who identified Ms Plame to select journalists? And if it was Mr Rove, directly or indirectly, there is the familiar follow-up: what did the President know and when did he know it?
So far, there is no evidence that Mr Bush is implicated. But if he was, the cover-up would constitute clear cause for impeachment. If he was not, he is surely still culpable for setting a tone in which such an abuse was permissible. Mr Bush came to office in the wake of Bill Clinton's impeachment, promising to restore honour and dignity to the White House. The investigation will show whether this was a promise too far.