Getting caught blackmailing a Congressman would be very, very bad for them. It's far more likely that money from a secret budget ends up in the campaign fund of friendly politicians, or that politicians who do what they want end up with lucrative consulting work after they leave office, much as it is with other industries.

But what do you propose to do about it either way? Go join Lawrence Lessig's anti-corruption campaign. In the meantime it's not like positive change is impossible, it's just harder than it ought to be.