I think you should pursue more a not so high tech dependant idea, like: Airbnb, Groupon, Yelp, this sort of thing.
This might apply to you: http://xkcd.com/1425/
EDIT: I think the NSA part was just a joke.
If you were starting from complete scratch, 15 years (assuming 1-2 people). But the reality is you aren't starting from complete scratch because the academic community in particular (and previous technology) have a great deal of prior work in this specific area.
So maybe 3 years until you have "something basic" and then 5 years until it is really profitable (presuming its accuracy rises year upon year). That's if you exploit all academic work you can find and try to build on existing technology as much as possible.
You could maybe do it in about 1.5 years with a large team.
I have found some open source algorithms that claim to have a decent amount of accuracy, though decent isn't enough it may be a start. What is your opinion?
Going as far as contacting the NSA, I don't know how willing they are in sharing their technology. I know they do work with private corporations which benefit both parties, I guess it would be worth a shot. That would be an interesting approach.
How long do you think it would take to build something like this? Even if we could just get sentiment values ie. Positive / neutral / Negative comments, that would be a great start and I believe much simpler.