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The Grand Asteroid Challenge is a project to capture an incoming asteroid, enter it into a stable Lunar orbit and send a manned mission to its surface.

That sounds... implausible at best. Do we have even hope of acquiring necessary technological means - like a vehicle capable of delivering enough delta-V to an asteroid to get it into an orbit and then prepare and send a manned mission (and this all until 2017)?

How do the scientists of NASA see the plausibility of this idea?

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Yes, if you find a suitable asteroid in a suitable orbit, it can be done. The asteroid would be meters in size, requiring a few hundred m/s $\Delta V$. Calculations on asteroid populations indicate that we can find such an asteroid.

From the paper referenced in the comment below (ERO = "easily retrievable object", where "easily" must be meant in relative terms):

Indeed, the paper presents a list of 12 EROs, with a total of 25 trajectories to periodic orbits near L2 and 6 near L1 below a cost of 500 m/s, and the number of these objects is expected to grow considerably in the coming years. The lowest cost is of 58 m/s to transfer asteroid 2006 RH120 to a halo southern family with a single burn on 1st February 2021. All the capture transfer opportunities to Earth’s vicinity have been identified for the currently catalogued NEOs during the next 30 years, and enable capture of bodies within 2-5 meters diameter with low propellant costs.

As for your question on schedule, 2017 is extremely aggressive even just for the launch of the capture mission, so probably not. I did not see that date in your link, so I don't know what it is referring to.

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    $\begingroup$ By the way, the "or" in the question title is not exclusive. It could be plausible and a PR stunt. $\endgroup$ – Mark Adler Sep 1 '13 at 2:19
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According to this reference

NASA associate administrator for human exploration and operations Bill Gerstenmaier said the use of “redirect” in the mission concept is deliberate, since they’re interested in objects that already would pass close to the Earth. “We take advantage of the fact that it’s already coming back so we don’t have to change the velocity in that direction,” he said. “All we need to do is essentially redirect it” into a lunar orbit, taking advantage of the Moon’s gravity. Left unstated was that redirection would also be useful if an object is passing too close to the Earth.

enter image description here

So I think is that it is possible since the asteroid is heading towards the earth the only thing we need to do is to catch it and redirect it to an orbit ( which may sometimes require adding or reducing velocity which require fuel )

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