It probably won't happen. NFL union shot down the 18 game idea, and that one didn't even extend the season since it cut into the preseason. Also, there are a lot of bad things about expanding the playoffs.
First, the NHL and NBA regular seasons are nearly insignificant due to being too permissive with their 16 team playoff slates. The NFL strikes a nice balance where making the playoffs is a challenge and shouldn't be taken for granted, while still allowing for a few non-elite teams to make it. So the product would be worse if it expanded. That's problem #1.
Second, I've given it a lot of thought and expanding the playoffs either means adding pre-wildcard round like major league baseball just did, or eliminating the bye week and having every team play in the first weekend. I think the first idea could be okay if the union agreed to it and bye week teams didn't mind having two weeks off instead of one, but the 2nd idea would suck. It would make playoff seeding far less relevant. Nothing in sports comes even close to fighting for a bye in the NFL. Given that road teams have done well in recent years in the playoffs, it would make seeding close to worthless and by extension, it would make the regular season far less compelling.