To be extremely frugal or careful with money; to spend as little as possible.
This phrase dates to the mid-19th century American usage, derived from the literal act of pinching or squeezing coins so tightly that it would be difficult to spend them. The imagery suggests someone gripping their money so firmly that parting with even small amounts becomes physically difficult.
The physical metaphor is quite vivid - imagine literally pinching pennies so hard that your fingers hurt, making it painful to let them go. This phrase emerged during times when pennies had much more purchasing power than today, so being careful with even the smallest denomination made economic sense for working families.
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