When the country goes bankrupt, which isn't too far off into the future.
^^^
I'm guessing something along the line's of Paul Ryan or W style privatization by the middle of this decade. Don't just look to the Republicans either.. There's plenty of Clintons and Kerreys in the party who were receptive to the idea before and could easily get on board when the party inevitably decides to 'moderate' and pursue 'bipartisanship' through 'austerity' measures.
Which idea? Stopping social security payments cold to the current elderly? I'd bet that even if every single Democrat were to disappear from the Congress and the White House tomorrow, Republicans wouldn't be able to pass it. Borrowing like drunken sailors to finance the transition (paying the benefits to the current seniors, while shifting to private solutions for the future generations)? And who is going to be lending, especially under the current conditions?
The fact is, whatever you think of the current system, it has a lot of inertia. Stopping it cold isn't feasible politically, and transitioning to another system would cost a lot of money and require humongous temporary expansion of the public borrowing. Long-term adjustment is another matter - I could easily see adoption of policies that would slowly transition, say, to individual private accounts, while letting the traditional Social Security wither through inflatoin. But it would take many, many decades for this to happen.
And, as for Medicare, though cutting costs is an urgent necessity, abolishing it is outright impossible (and "privatizing" would either save nothing, or would be tantamount to abolition), unless the society is willing to experience a major (admittedly temporarily) mortality spike among the elderly. Since many non-elderly voters have elderly parents, and since, if Medicare were to be abolished, they'd be solely responsible for their care, and since, given the tax incidence at present, for an overwhelming majority their expenses would dwarf whatever tax savings they'd be able to enjoy, the uproar wouldn't be limited to senior citizens. Florida would secede 
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Unfortunately, you are pretty much right. SS is a giant Ponzi scheme, and no one wants to be the one who is left with the bill without getting their share of the profits. The thing is, it has to end sooner or later, and the fallout of the end of SS will be much worse if it happens later. Nothing short of a giant economic crash or the Medicare/Social Security system becoming more expensive than the US military will be ending it.
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