Though I don't think you turn against your team when they fail, I don't personally adopt the "family" analogy. They are a football team who you cheer for, but when they fail, you have the right to be pissed and to expect them to do what it takes to do better. If they don't win, then they fail. That's the measuring stick for success in the NFL (Family members don't exist to succeed at specific tasks, and are not (should not) be judged as such in my opinion). Not playing hard or being good guys--winning. If they were in the "Friendly, Likable Team Olympics" then I think they could be judged on those merits, but you judge your team on their ability to win and to do what it takes to win. If not, why have teams have scores at all? Make it like pre-school kids playing and don't keep score. We have scores because this is a competition between teams to win. They play to win the game, not to make the fans happy except insofar as they can win games. If you win, fans will support you. If you don't, they won't. That goes for any team in any sport, and if the millions of millions of dollars aren't incentive enough for teams to win, that alone should be. Not the hope that fans will shower them with love when they fail. If they need support for being failures, they should go elsewhere, I say.
If you really believe NFL teams are like family, then how could you ever justify getting rid of older players or failing coaches? If you only focus on success, how do you identify failures and correct for them?
How many St. Louis fans are out there focusing on the positives right now, do you think? Or Lions fans? You can't expect them to do that, because there are so few positives to take away. If your team blows it at the end when it counts, then you need to focus on why they blew it, IMO. I will always root for my team, but I'm damn sure not gonna be all sunshine and cupcakes if they make stupid decisions and play like poo.
Also, pride is a deadly sin