I completely left out an important aspect of this debate in my discussion above. And now that I am being more aware of it, I'd like to add to what I wrote basically changing my stance that it is indeed legal for NSA to do these searches, even though it might not be constitutional or the right thing to do.

The important law is PRISM act that was passed in 2008 and renewed in 2012. This act allows such surveillance widening the scope of "foreign power."  This article sums it well: 
Not
http://www.theatlantic.com/national/archive/2013/06/prisms-legal-basis-how-we-got-here-and-what-we-can-do-to-get-back/276667/

Note the difference between "targetting" and "aquiring information."

So, the government has legal authority to do so; but I still think it is unconstitutional. Unfortunately, this cannot be contested in the Supreme court and the only way to repeal it is via Congress.