As Teaching History points out, it's likely that more than one military commander uttered the phrase "Don't fire until you see the whites of their eyes" or something like it because 18th-century armies would often be dealing with ammunition shortages, not to mention the inaccuracy of their muskets. A similar phrase is attributed to British General James Wolfe during the French and Indian War as well as Prussian soldiers during the time of Frederick the Great from the 1740s to 1780s.
Revolutionary War Journal reports that, according to several eyewitness accounts of the Battle of Bunker Hill, Israel Putnam wasn't at the front lines at all and was "safely tucked away from harm, some eight hundred yards behind the American line on Bunker Hill." If something like the famous phrase was actually uttered, it's possible it came from Colonel William Prescott (depicted in the print above) who commanded the redoubt at the top of Breed's Hill where troops held off two British attacks before succumbing to the lack of ammunition and retreating.
