If I were an NFL owner, I'd be trying to organize Goodell's firing or forced resignation.
He's shown, over and over, that he handles major decisions incompetently. When he started handling player discipline, he was criticized for sentencing that was either overly harsh or comically lax. When he dealt with the bounty scandal, he imposed harsh sanctions that weren't sufficiently backed up by evidence. Now, when dealing with something as simple and volatile as a domestic violence incident, he delivered a comically lenient sentencing and tried to make the evidence of Rice's crimes go away.
Even worse, as the above examples show, his decision making gets worse as the stakes get higher. At some point, the blowback from the NFL's poor handling of concussions will manifest. It will require an untold amount of grace, intelligent decision making, and resilience from Goodell to guide the league through that situation. He has shown that he posseses none of those characteristics. Goodell will find a way to make the obvious wrong decision. He'll find a way to take a volatile situation and make it explode. He'll cave and do something thoughtlessly at the worst possible time.
In the early 1900's, Teddy Roosevelt suggested banning the playing of Football. In the future, the game will face far greater and more publicized concerns about its future. And Goodell will be the one in charge of navigating that minefield.
The future of Football is at stake. Goodell must resign or be fired.