From the NFL rulebook, Rule 5, Section 1, Article 1:
The game is played by two teams of 11 players each. If a snap, free kick, or fair-catch kick is made while a team has fewer than 11 players on the field of play or the end zone, the ball is in play, and there is no penalty.
So from a technical standpoint, the Packers did not have to field any players, as they would not have received a penalty for not having 11 players on the field. They may have been hit with an Unsportsmanlike Conduct penalty, although since the game was over, it wouldn't have meant much. Rule 5, Section 2, Article 11 (emphasis mine):
Using entering substitutions, legally returning players, substitutions on sidelines, or withdrawn players to confuse opponents, or lingering players leaving the field when being replaced by a substitute, is unsportsmanlike conduct.
However, I doubt that fielding no players because of frustration would qualify as confusing opponents. Bringing the team back to defend the extra point was about Mike McCarthy's integrity. He wanted to stay professional despite miscommunications at the end of the game. McCarthy later stated:
We're in tune with staying true to the integrity of the Green Bay Packers. How we conduct ourselves, being professional during a tough time, during a challenge, a different challenge, but I'm excited about overcoming it. I look at this as an opportunity to put another feather in our cap.