If not blackmail, then some kind of extortion.
E.g., maybe the Obamaites threatened to have one of Petraeus's friends or compatriots killed. Say, someone who is currently serving in Afghanistan. And the Obamaites told Petraeus the dirty deed could easily be covered up by blaming the death on the Taliban.
Do you think Petraeus would agree to take a fall - to save the life of a friend? I think he might.