Blackmail is a gun you can only shoot once... Plenty of politicians have survived bigger scandals.
And don't forget the public is savvy enough about digital image manipulation that the evidence could be put into question long enough to get everyone through to the next budget vote, where all the three letter agencies get axed. Besides, a scandal only means no reelection... If you're obstant enough, you still finish out your term, and get to keep making laws.