I dont think social security will ever be cancelled. The question is what will it actually buy when your turn comes. By this I mean I do not expect it to keep pace with inflation as they print copious amounts of money to keep it solvent.
They can pay everyone $2000 a month, if a loaf of bread is $2000 if you catch my drift.
The tax rate itself is plainly a political choice.
The demographic issues are a consequence of political choices, e.g. the way we prevent working age people from coming to this country to pay into the system. (and now, kick some of them out).. but also, the ways that choose not to enable families to comfortably have children.
That's quite a tall claim to be making about a country built on immigration. The greatest periods of economic growth in the US are correlated with immigration rates.
I don't know what "proof" you have but remember that the economic impacts of demographic shifts are pretty broad, so I would suggest you validate that your source is taking that into account, and isn't intentionally biased for political reasons. The overwhelmingly predominant economic opinion is that immigration is very valuable in growing a country's wealth.