"What NASA should be doing is what no private enterprise can do: highly unprofitable risky space pioneering that inspires the human race."
http://www.redorbit.com/news/space/1112392431/spacex-sets-it...
I do not know if SpaceX will make it; I'd personally bet against that timeframe, though I wouldn't bet against the goal in general. But I will guarantee this: Barring a major political turnaround in the US, SpaceX will make a manned mission to Mars happen before NASA possibly could at this point. They don't have to make sure at least one part is sourced from each Congressional district, they aren't beholden to a Congress that on space exploration time scales blunders about like a drunken sailor, and they aren't a 53-year-old sclerotic bureaucracy.
Unprofitable they can do (and I mean that in both the good (research) and bad (blatant waste of funds) ways); they can not do risky. Unless you mean "risky because politics compromised the engineering process", which they can also still do. (Reading an honest history of the Space Shuttle is an eyeopener. Feynman and the glass of ice water was only the flashy tip of the iceberg. Google "Senate Launch System" for the latest.) It isn't in their genes anymore. You could put it back, but in the time that process would take, SpaceX will be there already.
There is no NASA apart from politicians. They are a wholly-owned subsidiary of Congress. That's not even a political statement, it's simply descriptive. If you can't trust politicians to drive our space policy, then you can't trust NASA to do it.