Taking all 32 teams would cheapen it. I hope the league is not reading the following hair-brained idea, because they will probably implement it.
Take the division winners (8) and the next best 8 teams by record, four in each conference (wild cards). The have a lottery drawing among the bottom 16 to randomly select 4 more for each conference. The 8 wild cards can play the 8 lottery winners, and the winners from that play the 8 division winners.
Make the lottery a two day event in Las Vegas, where they draw a team every 3 hours.It would sure generate fan interest among the teams not good enough to make the playoffs by record, even though we are taking half the frigging league based on their ability to not be one of the bottom half.
Oh, and we can give the 8 that do not win slots in the lottery all trophies, too.