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.