1590s, "prob. earlier in colloquial use" [OED], possibly a frequentative form of pock, dialectal variant of poke "bag, sack" (see poke (n.1)), which would give it the same notion as in purse (v.). "Verbs of this type often shorten or obscure the original vowel; compare clutter, flutter, putter, etc." [Barnhart]. Related: Puckered; puckering.
1726, literal; 1741, figurative; from pucker (v.).
: The U.S. ships were taking no chances: as Capt. Mathis told his crew members, one mine is enough to keep the pucker factor up
Fear; state of fright: Don't get into such a pucker (1741+)