This would require a good amount of coordination and risk. These politicians are pretty well connected. And I think that if one politician was threatened, they'd likely bring in many others for support. As much as politicians may hate those of the opposing party -- being blackmailed by the NSA would likely go too far and would be the quickest way to have congress shutdown the powers of the NSA. No one in congress is so naïve to think that the NSA blackmailing a politician could never happen to them.
That thought has crossed my mind, but I think the advantage of being well connected might not be enough.
A scenario: Imagine a powerful politician being approached by some shady guy in a trenchcoat who does not officially work for anyone. Shady guy produces some kind of material that, at best, is deeply embarrassing and personally damaging, and at worst, embroils said politician in a scandal that would cause professional damage, possibly even result in legal issues that this politician's power isn't enough to withstand.
Considering such a scandal is there to expose, said politician is probably not a paragon of virtue. Would this politician not bend to will of the shady guy? Even if he knew that shady guy is NSA, he could probably not prove it and exposing this knowledge would cause the damaging material to do it's job and only cast suspicion on the NSA.
I think the reason why the NSA could easily use information to blackmail politicians is that secrets are by definition kept hidden to as few people as possible. As such, these collectively powerful individuals can still be privately vulnerable, and are likely to opt for keeping their secrets over fighting some 'faceless' organization.
