The James Webb Space Telescope certainly is capable. A better question: given the limited time James Webb has to observe, what should we prioritize, what should be handed off to other (lesser, let’s say) telescopes, and what about all the stuff in the middle? For this we get a time allocation committee, just like lots of other telescopes have their own committees. The general STScI (Space Telescope Science Institute) has its own leadership, besides simple archiving and other administrative work.
One of the mechanisms at their disposal is ToO time (Targets of Opportunity). A small fraction of time is set aside for, well, targets of opportunity. Time-critical targets that cannot go through the normal proposal-review-revision-acceptance chain, because then the target would be gone. ToO includes things like supernovae, other outbursts like gamma-ray burst counterparts, and yes, risky asteroids. JW, like other telescopes, has ToO time, and a committee to judge such targets and their worth.
As it stands, a precedent is in place (as we saw) for asteroids judged to be an impact risk. But that’s one precedent. For future reference, there should be things like standards and protocols and procedures, so all this runs smoothly next time. (There will be a next time- just a question of when, and what diameter small body.) Therefore, the powers that be at JW are polling the science and planetary defense community. Submit a short (paragraphs) note on possible uses of JW at asteroids:
https://docs.google.com/forms/d/e/1FAIpQLSc_hiNz4elzpdtVva1gWxnB4iVb0azCTjuujjP5qhCM8atE5Q/viewform
The window will be open for submissions until Jan. 31.
See also: IRTF Survey