INTERVIEWER JEREMY HOBSON: Do you think it's possible that the private sector beats NASA in getting to Mars?
BEATTY: Not with people.
Orion uses a parachute to land, Red Dragon will use Super Draco based thrusters to land.
Nasa throws away the tanks used to get Orion to Space, SpaceX will land the tanks and reuse them to lower overall mission cost.
Nasa spent 60 billion dollars to get this far, won't be ready to test its new SLS system for 3-5 years, won't fly a human for 10+ years. SpaceX will fly astronauts to space by 2017.
SpaceX spent 3 billion getting this far and resupplies the ISS. Multiple times.
Beatty is short sighted and underestimates Elon Musk.
Alternatively, SpaceX hasn't launched people into space; NASA has. SpaceX hasn't launched a space station; NASA (and others) have. NASA has larger budgets, but they solve that problem by having larger budgets.
The hardest part about getting to Mars isn't flinging a metal tube off the Earth. That part we know how to do.
The hard part is keeping people alive for 6 months there, 6 months back, and providing all the equipment necessary to do meaningful science on the surface.
This isn't to say that an adequate launch system isn't essential to the mission, but I would be very surprised if SpaceX developed life support systems independently and more efficiently than NASA. More likely, I can imagine a news headline in which a SpaceX rocket sends a NASA capsule and living module to an off-world mission.
The actual spacecraft part is easy in comparison. It's of reasonable dimension, you can test and fiddle with it on the ground, and plenty of common practice is available due to submarines and high-altitude aircraft as well as decades of continuous operation in space.
The history of manned space systems will present plenty of examples of the booster being the pacing element. But we don't have to look much further than the very system we're talking about here. Orion is ready and flying a projected 4 years (and probably longer in reality) before its booster. And that's not because they got a head start.
That's not to say that rockets and manned space craft are similar problem domains; they're not. Any expertise SpaceX will need in that area will have to be developed separately. But the techniques are well known (thanks largely to NASA, who make no secret of it) and are just plain not that hard. They're already flying a pressurized and temperature-controlled Dragon (which spends time as part of the ISS), and are in development of a crewed one.
It is true that SpaceX has yet to operate any space stations, which NASA has, and which are the closest analogues we have to an interplanetary spacecraft. But again, ISS systems are a known quantity, and SpaceX could easily replicate them. Or, if they don't want to bother, could contract with Bigelow, who is currently flying two (unmanned) pressurized space stations, with designs for manned versions ready to go and awaiting a way to get there. SpaceX and Bigelow have already announced plans to partner for orbital station operations.
A Dragon and a Bigelow station would provide a nice ride to Mars. Getting to the surface and back would be a bit of a problem, but a SpaceX/Bigelow team could possibly land on Phobos and return in the next 5 years. And on a darn low budget, too. If you want to walk on Mars without too much tech development, Dragon 2 should be able to land just as it does on Earth. Dunno how you'd get back up, though. Maybe you could land a Falcon-ish booster loaded with a storable oxidizer (like peroxide) on little enough juice that it could get back into orbit. Haven't looked into the numbers there; F9-1 is certainly single stage to orbit on Mars, but down-and-up on the same fuel load seems unlikely. It'd certainly work with ISRU propellants, but that's a nice can of worms.