I actually think both Bush and maybe Clinton were looking at something like 5% of total funding being invested in the stock market.   That would be huge windfall for stockholders in the first year as it would create buying pressure, but after that, I don't see it as such a big deal.

In my my own self managed retirement with Pella Corp, each employee had several investment options over the years, including 100% in stock funds.    Sure it mean some people lost money and some people made more money, but stocks overall outperform bond funds, (NOT true over every 10 year period).

I think 5% of social security being in the stock market would be fine.  It would force some money into long term holding, not sure that fits the pay as you go structure of today.