This isn't just a government problem either; people in europe are at least as unhappy about firms like Google and Facebook warehousing their data, but at least over in Europe they have robust privacy laws that service providers have to comply with.
See for example these stories, in which (some) American users express puzzlement over Euros' insistence that they are the owners of their personal data:
https://news.ycombinator.com/item?id=3127185
https://news.ycombinator.com/item?id=3867166
https://news.ycombinator.com/item?id=3036157
There's a Facebook bias to these because those were the easiest threads for me to remember & get search hits on, but the principles apply to any firm that retains customer data. EU users have a legal right to demand companies divulge all dta stored about them, and insist on its permanent deletion - something that's not available to US users.
Now, you can hardly insist that governments be less powerful than the companies they are supposed to regulate. If you want real privacy, then you need it explicitly stated in law, and structured so that it can't be signed away in exchange for some commercial benefit, much the same as you can't legally sign yourself into slavery; such contractual arrangements are inherently invalid. This is going to require a constitutional amendment, because otherwise companies are going to defend their data hoarding and unilateral exploitation of said data on First Amendment grounds.