Assuming the show won't air live and across the country, one would assume there won't be any 'real time' winning going on here (e.g., "the first person to call in nationwide with a Bingo wins $1,000,000!")
Now, assuming there won't be the ability to design-your-own-Bingo-card through some online entry, ABC could 'create', let's say, 25 cards on line, and you'll register on their web site to participate, at which time you'll select one of the 25 cards to be your own. Numbers will be drawn until at least one of the 25 cards has a Bingo on it ("Caesar says STOP!"), and then all those who picked that card are now entered into a drawing.
Perhaps they could sweeten the pot by allowing the registrant to select a card for each of the 3 rounds, and if he/she gets Bingo on that round's card all 3 times, is entered into a drawing for the grand prize.
With 25*25*25 = 15,625 different ways to pick 3 cards, one would expect hundreds of entries for the grand prize. Even if you don't restrict the number of times a home viewer can enter and play, that number is prohibitive enough to prevent someone from trying to enter every possible combination.
You can still offer nice prizes to winners in game 1 or 2, but getting more than one Bingo during the night ought to be worth something. Give away a quarter million in prizes and make a nice profit off the ads, esp. if you keep production costs low (maybe they can borrow the Lingo set and have a model draw the numbers).
I look forward to seeing how ABC will attempt this...
Matt