Plot idea is rather common; I've seen more than one story like this of Kuttner alone.
Story summary.Most of the story is a creepy one - a man has convinced himself that there are aliens among us, aliens in the shape of humans, aliens who intend to take over earth. And that these aliens cannot be killed; they get resurrected. Of course, he's unable to convince anyone.
There is a surprise ending, but may be I've already spoiled it.
Fact sheet.First published: Galaxy, November 1956.
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Related: Stories of Lester del Rey.