It is not, however, the full contribution for the employee. Nor is it the "Ryan Plan"...
The most they could invest under the Ryan plan is that 1/3 number again and also over a long time frame...
http://www.lwv.org/content/federal-privatization-ryan-plan
(from the link: “A Roadmap for America’s Future” contains a plan to privatize Social Security. That plan would give workers under age 55 an option of investing about a third of their Social Security taxes in personal retirement accounts. It would guarantee that the account would never be less than the amount placed into the account plus inflation. The account would belong to the individual and could be inherited. Individuals would invest a portion of their contributions in a limited number of funds managed by the federal government. That portion would increase over time to a maximum of 5.2 percent of the current 12.4 percent Social Security payroll tax. Retirement age would very gradually rise to age 70, instead of age 67. In addition, a one-time payment of $2 billion would be required to assure continued benefits to those over age 55 and others not participating in the privatization plan.)