Some people are perfectly happy with their government violating the Constitution every day in order to spy on them. All they need is for somebody in big daddy government to pat them on the head and say, "We're doing it for your safety."
What is vital to recognize is that the NSA is collecting and storing staggering sums of communications every day. Back in 2010, the Washington Post reported that "every day, collection systems at the National Security Agency intercept and store 1.7 billion e-mails, phone calls and other types of communications." Documents published by the Guardian last week detail that, in March 2013, the NSA collected three billions of pieces of intelligence just from US communications networks alone.
In sum, the NSA is vacuuming up enormous amounts of communications involving ordinary Americans and people around the world who are guilty of nothing. There are some legal constraints governing their power to examine the content of those communications, but there are no technical limits on the ability either of the agency or its analysts to do so. The fact that there is so little external oversight is what makes this sweeping, suspicion-less surveillance system so dangerous. It's also what makes the assurances from government officials and their media allies so dubious.