in Shirtless Football Game
The pics were snapped New Year's Day at the Kaneohe Marine Corps Base on Oahu, where the President and the first family stayed for their 10-day vacation.
Obama -- who's pretty ripped for a 50-year-old -- makes some shockingly athletic plays ... diving for catches, tossing up some Hail Marys, and juking people all over the place.
When was the last time a President did THAT?!?
Obama and the fam arrived back in DC early Tuesday morning -- where Mr. President will begin to quarterback his re-election campaign.