古フランス語のpoulser「押す、推進する」から。ラテン語のpulsare「打つ、打つ、推進する」が語源で、語源的にはpulse「推進する」と同じ。
"Pushing up the daisies now," said a soldier of his dead comrade. ["The American Florist," vol. XLVIII, No. 1504, 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. To push up daisies "be dead and buried" is from World War I.