No they won't. Because most people do not care about their privacy. If you expose the average consumer/voter/citizen to someone who has a way with words and is not above embellishing the truth a bit, they will gladly accept the government snooping on them. Gladly. Every time.
Most people lack the intellectual fortitude to imagine why having no privacy may be a bad idea. Most people like it in the herd. Most people like being told what to do and will complain bitterly if you expect them to think for themselves. Most people are morons.
I'll give you an example. In Norway we let parliament introduce data retention laws that will make it possible to map your every move and everyone you communicate with. All the metadata from your phone records. If you want to know what that looks like for just one person have a look at this example from germany (click the link to see the demo):
Green party politician Malte Spitz sued to have German telecoms giant Deutsche Telekom hand over six months of his phone data that he then made available to ZEIT ONLINE. We combined this geolocation data with information relating to his life as a politician, such as Twitter feeds, blog entries and websites, all of which is all freely available on the internet.Save for a few scattered protests, the Norwegian people signed up for this. We want the government and all its agencies to know where we have been and who we talk to. We do not want privacy. We elect people who take away our privacy and we do not think twice about it. If we really cared about this we wouldn't elect these people -- so obviously we want the government to snoop on us. It is our own damn fault.