But, there's just one flaw in the promotional plan: Hamilton was never president.
Hamilton is considered a Founding Father and was the country's first Secretary of the Treasury. He led the development of the economic policies of President George Washington, one of today's actual honorees, and the nascent nation. 
It's just too bad there isn't Treasury Secretary Day to have sales in his honor.
An inquiry on Monday morning garnered this response from a spokesman:
"Groupon is always very serious about helping our customers save money, and saving $10 is no laughing matter."
The spokesman later confirmed the mistake was an intentional stunt.
"Most Presidents' Day promotions make people fall asleep, so we wanted to do something different that was in line with our brand and sense of humor that got people talking and writing about Groupon," he wrote in an email.
For what it's worth, Groupon said the fake was "an overwhelming success" in terms of marketing exposure and tweets.