The gold coins commemorate the 50th anniversary of the John F. Kennedy half dollar.
Initially, the Mint said it would make a limited number of sets available each day, Tuesday through Friday.
However, early Thursday morning, a Mint officer told 7NEWS this will be the last day they are available.
The Mint gave out 100 tickets to the first people in line, allowing them to purchase the coins.
However, people weren't officially allowed to line up in front of the Mint until 6 a.m. At 5 a.m. there were already dozens of people gathered across the street, ready to make the dash for the tickets.
"Crazy, bananas. B-A-N-A-N-A-S," said one successful man, as police worked to keep the crowd calm. "I got trampled, I fell down, I got back up. Because I'm a soldier."
A total of just 800 of the proof sets were available.
The 24-karat gold coin first went on sale Tuesday morning -- for $1,240. Some buyers said they were paid as much as $600 to stand in line for the coins.
-- About the coins
One side of the coin bears a portrait of JFK designed by former United States Mint Sculptor-Engraver Gilroy Roberts. The Mint says the profile was based on a portrait prepared for Kennedy's presidential medal and was originally designed shortly after Kennedy's assassination.
The other side is based on United States Mint Sculptor-Engraver Frank Gasparro's rendition of the Presidential Seal, surrounded by a ring of 50 stars.
According to the Mint, the coins are contain three-quarters of a troy ounce of .9999 fine, 24-karat gold and were struck at the United States Mint's facility in West Point.
The coins also went on sale at U.S. Mints in Philadelphia and Washington, D.C.