In his new book, Constitution 3.0: Freedom and Technological Change, Jeffrey Rosen measures how endangered that right may become. He imagines a scenario where websites like Google and Facebook could "someday potentially post video from live surveillance cameras online — and then archive those videos in a database," which combined with facial recognition software, means police could easily identify most citizens. As unlikely a scenario as it is, according to Rosen, it's also not prohibited in the Constitution:
Facebook is a private actor, the Constitution and the Fourth Amendment only prohibits unreasonable searches and seizures committed by government actors. … I think that helps crystallize the fact that at the moment, lawyers at Facebook and Google and Microsoft have more power over the future of privacy and free expression than any king or president or Supreme Court justice. And we can't rely simply on judges enforcing the existing Constitution to protect the values that the Framers took for granted.
The Dish 