It could be fixed if the politicians wanted to fix it.
The SS trust fund is only short about $4 Trillion, the unfunded liabilities are much higher than that, but the issue is making the trust fund solvent, so the monies paid in can be paid back out to retirees.
That isn't difficult at all to do, the Federal government holds considerably more than $4T in assets, they own land, lots of land, land with known deposits of coal, oil, timber, etc., land that could be used for Nuclear power plants, the airwaves, offshore mineral rights, all kinds of things the federal government owns.
So transfer $4T of those assets into the SSTF, Maybe more since there should have been interest earned on all that money, instead of not even meeting inflation in government bonds that don't even trade in a marketplace, rip up half the national debt (the SSTF would "pay" for these assets with the debt instruments it holds), and appoint or elect a board to manage the portfolio of the American people.
There's still a substantial surplus in SS revenue, over the next few years there would be nearly $1Trillion in cash to use to develop those resources and create long-term revenue streams,(if you kept congress from spending it) while solving or at least helping to solve our energy dependence problems. Nuclear plants, coal liquification plants, and ANWR would be good places to start.
Then the return would be based on the revenue stream once the payroll taxes no longer met the costs of the program, no more fixed income, but a dividend yield instead.
It's not ideal, but it's better than screwing everyone who's paid/paying in over completely by either doing nothing and letting the system crash or crashing the system intentionally.
The GOP plan isn't a solution because all it does is add ANOTHER forced investment system in the form of private accounts to the equation, it actually makes SS less solvent than it is now. The GOP plan would work just as well if they just instituted the means testing and benefit cuts without mandating the private investment in vehicles of the governments choice, but that wouldn't go over very well politically so they continue to try to convince you it's something other than what it is.