late 14c., from Latin pus "pus, matter from a sore;" figuratively "bitterness, malice" (related to puter "rotten" and putere "to stink"), from PIE *pu- (2) "to rot, decay" (source also of Sanskrit puyati "rots, stinks," putih "stinking, foul, rotten;" Greek puon "discharge from a sore," pythein "to cause to rot;" Lithuanian pūvu, pūti "to rot;" Gothic fuls, Old English ful "foul"), perhaps originally echoic of a natural exclamation of disgust.

early 14c., from Old French poulser (Modern French pousser), from Latin pulsare "to beat, strike, push," frequentative of pellere (past participle pulsus) "to push, drive, beat" (from PIE root *pel- (5) "to thrust, strike, drive"). Meaning "promote" is from 1714; meaning "approach a certain age" is from 1937. For palatization of -s-, OED compares brush (n.1); quash. Related: Pushed; pushing. To push up daisies "be dead and buried" is from World War I, but variants with the same meaning date back to 1842.

"Pushing up the daisies now," said a soldier of his dead comrade. [The American Florist, vol. xlviii, March 31, 1917]

To push (someone) around is from 1923. To push (one's) luck is from 1754. To push the envelope in figurative sense is late 1980s.