Not to be a double downer, I don't see the current president signing anything that would limit executive power so it would take 2/3rds of both houses to override a veto.

I concur, with the slight modification:

  s/current/any/;

Not only that, but any bill that successfully passed could, given past history by several presidents, be effectively ignored via executive order.

That one's easy to get around. Congress does budgets. If Congress has backbone (but not 2/3 majority backbone), they can pass a budget that de-funds NSA to whatever degree desired. The president can veto it. But then there's no budget, so there's still no money for the NSA...

The easy part is that would take only 1/2 of one chamber. the hard part is forcing a government shutdown is risky business, and maintaining the resolve of the caucus becomes more difficult the longer one drags on.

And whoever's opposed to it can easily spin the action as a reckless disregard for America's security. (Nevermind I think the NSA could disappear tomorrow in a puff of logic and nobody would be the worse..)