According to my game comparison, blackjack players play about 70 hands per hour. The probability of a blackjack in a six-deck game is 24*96/combin(312,2)=4.75%. I assume a blackjack tie still gets a stamp. So it should take about 30/0.0475=632 hands to fill the card, or 9.02 hours.
The probability of filling the card in 4 hours, assuming 280 hands, is 1 in 30,000 playing one hand at a time. I suspect any player achieving the goal in four hours was playing at least two hands at a time.
This question was raised and discussed in the forum of my companion site Wizard of Vegas.