I think this is the only way to fix the problem, permanently. The problem is that those younger taxpayers will have to make some contribution, with no hope of getting any benefits. Perhaps one way would be to divert the employee payroll tax into a 401(k), and continue the employer payroll tax for Social Security.
But, that's just a "broad stroke" proposal. There are other components of Social Security that must be addressed: survivor and disability benefits.
Coincidentally, the SSA did evaluate a proposal like this back in 2005:
Estimated Long-Range OASDI Financial Effects of a Proposal for Individual Social Security Investment
And another one, with a gradual shift of taxes to contributions:
I haven't yet waded through all of them, as there's a lot of info.