The population problem isn't one of absolute numbers, but of ... ... Actually it's an income disparity. Unlike Europe or Japan, the US has corrected it's Baby Boom population imbalance (at least in raw numbers) through immigration.
Although there is not a shortfall of workers to pay Social Security taxes in later years, more of those workers earn lower pay scales so there is a projected shortfall in tax collected. The normal economic outcome of this would be wage inflation with lower returns on savings.
This will advantage workers at that time. It will also advantage those who did not save for retirement and rely only on social security at th expense of those who did save large amounts.
Reducing Social Security benefits will advantage savers at the expense of those who did not.
That's my read of the real situation. The only alternate income is to bring in greatly increased numbers of immigrants at that future time.
If this is difficult to envision, just think of an exaggerated population imbalance. If nursing homes employed the same ratio of employees, there would be no employees to work in other sectors of the economy. The result would be increased wages. The workers could afford the increased cost of goods with their increased wages. The elderly after paying so much more for food and other expenses would be unable to employ the same amount of nursing care. Only the very wealthy retired could afford nursing care.