Most of what the Repugs are saying is simply trying to stampede people into accepting that there is a crisis and that their "privitization" is the answer. If there is any respectable core to their arguments it is that similar funds placed in the stock market have had a long term rate of return that is greater than treasury bonds.
It is not entirely clear that the superior stock growth assumption would be true if large quantities of funds had been diverted into stocks over the last 25 years, but grant for a moment that it might be the case.
It actually might make sense to put some portion of the trust fund into a broad index fund, not at an individual account level, but rather like an insurance company (what SS is anyway). The returns could be managed such that a portion of the dividends and capital gains could be drawn down periodically for disbursement as benefits. Because it would be a broad index fund the operational costs would be very small. There would, of course, have to be public rules about how the fund would buy and sell so there would be no insider deals.
The SS payroll tax probably does create some distortion in the labor markets making it more expensive to hire than without the tax. If the long run returns really are higher for stocks, then at some future time it would be possible to reduce the payroll tax or increase benefits to retirees. At any rate, the benefit structure would rest on a blend of wages and investment returns.
Such a stock fund would have to be insulated from political meddling (difficult but possible) and it would also create an investment bias in favor of companies that are in the index. If the fund were sufficiently broad and were defined by clear criteria the distortions would be minimal.
Such a counter proposal would preserve the essential insurance nature of SS but would call the Repugs on the plausible claim that assets are a better than wages for funding long term liabilities.