1660s, "an ant," from first element of pismire (q.v.) + ant. Meaning "contemptible, insignificant person" is from 1903.

[B]y sun-down [the gals] come pourin out of the woods like pissants out of an old log when tother end's afire. ["Dick Harlan's Tennessee Frolic," in collection "A Quarter Race in Kentucky," Philadelphia, 1846]