Will the change from pensions to 401(k)s drag down the US Stock market?

I will attempt to ask this as clearly as I can, but I’m curious as to what the long-term effects will be, and when they will rear their head, of the generational trend of going from pensions to 401(k) that has occurred in the American workplace over the last 30 years. Specifically, every time a stock is traded there must be somebody on both sides of the trade.

For generations, large pension funds paid out monthly payments to retirees until they died, around 30 years ago, the American employers started getting rid of pensions and transitioning all employees over to 401(k)s. As 401(k) employees begin to reach retirement age, they will have to start selling off assets in their 401(k)s for income in retirement. When this trend begins, will there be enough selling pressure on a continuous basis to stifle the US stock market?