The idea that social security is "broke" is something that was concocted by politicians who are fond of raiding Social Security to pay for their pet pork barrel projects. It would be doing just fine if the money paid in were left alone and allowed to grow and remain to pay those who have paid in. A slight, slow, gradual raising of the retirement age might be necessary to account for longer lifespans, but that is entirely different and entirely more reasonable and fair than just abolishing the program entirely.
Social security is failing but it is still working. People will receive money, they will just receive less than they anticipated. The social security system requires massive adjustments that will come at the expense of the American people. With that being said, the system is still a good idea and it should be reformed.
Social Security isn't just a benefit, it's the law. If Congress chooses to suddenly take away people's Social Security checks, lawsuits will be filed to challenge previous obligations. Workers today will see their benefits provided. If the cost of living goes up as expected, Social Security payments won't go as far as they do today. Even if the system is broken now, it will be fixed somehow.
If Social Security was run by private individuals it would be labeled a Ponzi scheme. It was designed in a time when the average worker outlived his retirement by a few years, not a few decades as now. Unless the government radically overhauls the whole system there is no way that the money coming in one end will be enough to flow out the other end.