Maybe a small point for the superhero RP: There are dozens of organisations and hundeds of satelite/observatoriess trained at all parts of the sky, tracking tens of thousands of asteroid, comets, meteor candidates and so forth, and NASA isn't even involved with the few of them that are US-based - NASA's mostly about getting rockets and probes out there.
A more viable explanation than NASA just happening to miss the meteors would be that an intense solar flare irradiates earth and fries the electronics involved in those observation facilities (either the networks between them or the actual equipment), thus rendering them unable to keep a lookout for potential impacting objects.
With one side of the Earth fried (the side facing the sun at the moment the solar flare struck), if you had impactors sufficiently strike that side you'd send up debris and dust into the atmosphere which would naturally spread around substances that were already irradiated to basically every corner of the world.
And in general NASA has very little to do with anything organic or mutagenic and likely wouldn't in this case, but you could reasonably make the case that NASA exobiologists might be involved in leading the charge for the cure against the mutated.