They don't even have to say anything: she knows her job depends on co-operating. Bottom line is that she doesn't own Yahoo, she is a servant of the shareholders - she is expected/obliged to put their interests first.
OK, she could decide to not comply, or blow the NSA's cover on the extent of spying, but if she took Yahoo into direct conflict with the Federal Government over a personal opinion I doubt she'd stick around in the job for 24 more hours before the board decided she had to go.
It's the kind of kind of grandstanding that Jobs might have got away with (what you gonna do, fire me?). Zuckerberg is an interesting case: he still owns nearly 25% of Facebook, so his chances of being summarily fired are less. Still, I find it hard to imagine a CEO deliberately risking jail and being allowed to continue to serve (as the share price plummeted)
No need for threats and blackmail: the market does it for you...