Actually, the Republican Party has been going at it for a long time. The earliest attempt as far as I know to privatize social security is during the Bill Clinton's administration. It eventually got derailed after Monica Lewinsky scandal became the center of political discourse. Of course, Bill Clinton's "welfare to work" is a classical Republican idea that only adds burden to the low-income people.
The GOP has tried to privatize social security under the Bush administration. It failed. But this undying "dream" of GOP is going to haunt us again in the near future, when the tax cut will dramatically increase the deficit. By then, "the deficit hawk" side of the GOP will complain about the growing national debt, and demand to cut funding for government programs, such as medicare, medicaid, welfare, and social security in the name of balancing the budget.
I was reminded of this GOP trickery by Rational National:
Bernie’s Prediction On Tax Reform Comes True
Sanders Challenges Republicans to Prove Him Wrong About Tax Bill