First of all, from the league's perspective the timing of the event couldn't be much worse: it happened during a nationally televised Monday night game, after a weekend where there were already several nearly inexcusable gaffs. Second of all, the refs really couldn't have picked a worse team to shit on: the Packers are one of the most popular teams in the league, and were early playoff favorites. That's going to mean much more lost revenue than if it had happened in, say, a Seahawks-Rams game. Even if the NFL itself doesn't take an immediate revenue hit, the teams will: fewer people will buy game tickets, and less merchandise. Other subsidiary industries will too: Vegas lost a bundle on the outcome, for example.
On the other hand, the league probably feels like it can't given concessions in negotiation: as Peter King has explained, the NFL is asking to reduce pension contributions for the refs, contributions that they have already reduced for their full-time employees. League officials probably feel that there will be blowback around the office if the refs successfully negotiate to preserve their pension benefits (I might point out that cutting benefits for anyone working in a business as ridiculously profitable as the NFL seems awfully damn cruel, but that's just me). Especially given that the league already has something of a tendency to keep going in the face of public criticism, I think they might decide to turtle in the face of public criticism and try to wait it out.
One thing that I think is interesting about the conversation is that in order to denigrate the scab refs, we basically have to exalt the union refs. We have to assume that things will be immediately better if they are reinstated, and that there will not be blown calls again. Even though the union refs themselves have previously decided the fate of NFL games for the wrong team, through either one or a series of calls. This isn't meant to say that the union refs aren't better than the scabs: the evidence so far is that they very clearly are.
In fact, this is a really interesting thing to be happening on the political stage during an election year, and I wonder if it will have an effect on any of the election races (though it will certainly be difficult to measure). The contrast between the scabs and union refs is a very public example of the potential difference in product quality between the union and non-union labor. While certainly not the referees intent, people understanding that contrast might give them a greater appreciation for unions, generally. This might be a good time for those unions to get their message out, as they might find a more receptive public now.
Also, the sports media have been leery of the replacements from the beginning (with good reason), and are not going to get quieter in their calls for the reinstatement of the union refs as the season goes along. What will change, sooner or later, is when players and coaches get more and more involved, and social and traditional media gives them a signal boost. Already, some players are willing to risk the fine from the NFL offices for speaking out against the refs (I've seen TJ Lang tweeting his rage, and there are probably others). How soon until it's an entire unit? A head coach? An owner? We could get to the point where the NFL loses any semblance of control of the situation, because either they can't fine everyone who is pointing out the obvious, or the fines stop being a meaningful deterrent to those that are going to speak their mind.
All in all, as much as the NFL might wish it were so, the controversy isn't going to go away, and the longer it goes on the more likely they are to suffer a significant drop in revenue for this and future seasons, possibly far eclipsing the ~3 million/year in pension benefits they are trying to avoid paying. Even though it may gall them, they have to understand that they've probably lost, and make amends while they can.