Only select people under investigation would have their entire text message conversations read by a human.
Does the NSA store all text messages? Yes, more than likely. Do their employees snoop on US citizens? Nope. Can other agencies have access to this data? Yes, Patriot Act.
There is a very easy way to test their capabilities. Send a text message with keywords involving bombs and political figures and see what happens. I'm not going to do it, but it would be an interesting experiment.
Information is critical in the world we live in. It's troubling that any secretive organizations would be able to have this much power over citizens, but the alternative is much scarier. The US has to maintain information dominance on the internet. Allowing other countries to dominate the internet could tip the scales of power. The US carries the big stick right now, if China gets the upper hand (and they are trying unimaginably hard) then what? What will the sleeping dragon do? I have nothing against China at all, but the unknown is scary and I simply would rather the US maintain indisputable dominance.