if you think this will cost Carson any support then you don't understand the people who support him at all or why they do so
Carson's supporters don't need really need to turn on him, though, they can just move on to saying that they'll vote for Cruz or whoever while still liking Ben Carson a lot.
IIRC polling shows that Carson's (national) vote share is pretty soft. The fact that polls show his support plateauing or peaking about a week ago probably hurts, too, in terms of how this will be covered.
