I doubt that. I'm sure they anticipated this response, but I think you greatly underestimate how many people subscribe to the "nothing to hide" theory of privacy and/or are genuinely worried this might aid pedophiles or terrorists.
I can't see how you'll see a backlash against the companies on the move, if only because there's no real competition and no value in being "the phone the authorities can easily monitor"
The worst case scenario is that they get large amounts of press (not all positive), fight for the rights of their users to have private data, and lose to a government they never expected to defeat. That's still a win.
