It's a mistake because targeting a journalist's family member is quite likely to piss the average journalist the fuck off. The Washington Press corps can make Obama's life fucking miserable if they so choose, and absolutely drown his agenda in press about Snowden, Greenwald, how and when the White House communicated with the UK about this, and a million other things.
They can make an oxygen-sucking scandal out of nothing. This could devour the rest of Obama's second term if it gets out of hand (and the Republicans decide there's more mileage in beating him up about it rather than supporting the security state).
The public does not have to care for this to be a huge negative for the gov't. The only people who need to care are precisely the ones most likely to--folks rather like Greenwald.