They do but people support a lot of things when they aren't presented the costs or tradeoffs. Support for all kinds of government spending goes down when any context regarding tradeoffs is provided.
If young Americans understood that they're effectively paying almost double the amount they see in FICA, and understood what that amount should get them in retirement if they saved that amount (less the cost of disability insurance), and understood all they are getting is a "promise" that future workers would be taxed to give them money, I'm not sure how many would support it.