Before the days of indoor plumbing, bedrooms were equipped with chamber pots, wide-mouthed vessels used by the room’s occupants as toilets during the night. Chamber pots were a common house-ware item for centuries, but the saying itself dates only to 1905. However broke people might have been in the past, there weren’t a whole lot of them unable to afford vessels to pee into.
“Not having a pot to piss in” is a 1900s idiom, distinctive in that piss isn’t metaphorical, or an intensifier, but literal. The full saying is “So poor she or he didn’t have a pot to piss in or a window to throw it out of.” It was found in the 1934 typescript of “Nightwood,” a novel by Djuna Barnes, published in 1936.
Piss is an old word in English and arose in the late 1200s, from similar words in French and Latin, according to the Oxford English Dictionary. For centuries, the word was regarded as informal but not especially naughty.
Some piss–compounds are almost as old as the original word. “Pisspot” goes back to the mid-1400s; “piss-burnt” (discolored by urine, which was often used in tanning and dyeing) dates to the mid-1500s; “piss-prophet” (one who diagnosed diseases through examination of urine) and “piss-house” (a privy) appeared in the 1600s; “piss-proud” (having an erection due to a full bladder) is from the late 1700s.
“Piss-elegant” (affectedly refined) was first recorded in 1947. To “piss away” (money, for example) is from 1948. The OED gives the first usage of the British “to piss off” (to go away) as 1958; the US version (to annoy) in 1968, although it’s said to have been in use during World War II. Ditto for “to take the piss out of (someone),” a British (and Commonwealth) idiom meaning “to satirize,” which first appeared in written form in 1945.
It is true that urine, which is acidic, was once used in tanning leather. It helped loosen tissue and hair that remained on the skins and softened the hide. Urine was also used in production of dye and of gunpowder and for other purposes. But these uses all but disappeared in the 1800s with the advent of modern chemistry and the ability to produce artificial substitutes cheaply and efficiently. So this old practice is not the origin of the phrase “not having a pot to piss in,” which appears long after the practice of using urine in industrial production had ended.
Having grown up on a homestead with no indoor plumbing, I’m familiar with both pisspots and pisshouses, though we called the latter an “outhouse.” We had windows, though!