I would imagine here in the UK our politicians will use this narrative:
* Evildoers aren't born knowing how to use tor and having all the right onion urls memorised. New recruits are onboarded/radicalised with tools the average person regularly uses. Like facebook, twitter, gmail, https-encrypted websites and so on.
* Active terrorists learn to use encryption properly before they start committing crimes, so we can't monitor the active terrorists. As our only option is to monitor new and prospective recruits, we'll have to monitor people who aren't yet committing any crimes. As we'll be monitoring the widest part of the recruitment funnel, monitoring huge numbers of innocent people is just the only option.
* People might be recruited through channels we're not already aware of. When a terrorist is recruited we need to be able to find out how they were recruited, so we can find new channels we need to monitor. And it could be months or even years between the recruit learning to use effective encryption and them being identified as a terrorist. So we need to store an internet history for every person for several years.
* Privacy? Well, there will be strict legislative safeguards in place of course! Unfortunately all the work will be top secret so only insiders can audit compliance and it'll be illegal for them to take any evidence of wrongdoing to the press. But the legislative framework will be very strict, yes sireee.
* This is the best option we have to keep our children safe http://www.bbc.co.uk/news/uk-31575908 you wouldn't want any more schoolgirls going off to join ISIS now, would you?