I'll also note that Americans in particular seem unusually susceptible to the belief that everyone else is wildly profligate and immature about wanting things for free but I personally understand that only the most painful alternative is the one that can work in reality. It doesn't matter how many studies show people under report pain, we are convinced that "people" (but not us personally) overuse pain medication unless sharply restricted. Despite studies that show widespread reluctance to enroll in poverty programs, and the stigma attached to them, we know that "people" will always prefer to get on the dole rather than work.
So the idea that we must do something painful for the sake of our future fits the broader pre-existing narrative, as well as making sense generally.
So the person who believes that "well of course the problem is the population is aging and the system was never designed for this" will read every study and watch every debate from this perception. The simplicity and intuitive sense of the "cut medicare to save it" narrative is much easier to understand than "well, but when you look at this data -- which you aren't going to read -- that just isn't true." Even if the average viewer sees a debate between two sides of the argument, and even if the person notices at the time that the "raising the Medicare age won't help" person makes some good points (or the other way around), that will soon be quickly forgotten and even the memory of the debate reshaped in accordance with expectations.
So how do you actually change public policy debates?
1) Time. Really. I'm sorry, there are no shortcuts. All true advocacy is culture change, and everything else is just fiddling at the margins.
2) Reframe narrative along value lines that set up an irreconcilable conflict for the listener. If we have conflicting values, e.g., planning for the future v. fundamental fairness (if we like that value), this causes people to re-evaluate the underlying evidence so they can break the tie in favor of the overarching principle. True, they may break the other way and look for reasons to explain why this isn't fundamentally unfair (or why, if it is, it's still the thing to do). But before you can convince them, you need to get them out of the groupthink and reexamining the basic premise.
3) Find the right messengers that give permission to rethink things. People take their cues not just from those around them, but from certain other figures. When Obama said he had changed his mind on same sex marriage because he had reconsidered things over a long period of time and had come to a conclusion that he had been wrong, that gave permission to a lot of other people to do the same thing. Yes, again, it could break the other way. Which leads me to my last point.
4) There is no sure way to win. Sorry. "It is a cruel world, and virtue is only triumphant in theatricals." (A quote I am sure I have mangled). A lot of successful advocacy is being willing to invest huge effort in creating the possibility for success.
No one in the advocacy world likes this, which is why so many people screw up their advocacy. They refuse to make the long-term investment. They take direct stands that have no chance of winning today because that seems safer than creating the opportunity for a better chance tomorrow. And, of course, all of us in public advocacy are subject to the same problems outlined above. It is intuitively easier to advocate directly than to seek to change culture. We accept the existing culture as it is and not something we can change. We see evidence of the triumph of our opponents and discount signs of our own success in changing the culture.
This is not to say things are hopeless. But it takes a considerable amount of effort.