c. 1200, demuren, "to linger, tarry, delay," a sense now obsolete, from variant stem of Old French demorer "delay, retard," from Latin demorari "to linger, loiter, tarry," from de- (see de-) + morari "to delay," from mora "a pause, delay" (see moratorium).
Modern sense of "raise objections, take exception, have scruples" is by 1630s, from a legal sense attested from the 1620s: "admit provisionally the facts of the opponent's proceeding but deny he is entitled to legal relief," a verb from demurrer. Such a pleading effectively stops the action until the point is settled. Related: Demurred; demurring.