The answer from this paper from the National Bureau of Economic Research might surprise you.

Does it pay to save? The answer is often no. In fact, penalties for saving are astronomical for some households, particularly young, single-parent and lower-income families. But these are the very people who need the strongest incentives to save for retirement.

For example:

A 30-year-old single parent earning $15,000 a year faces an effective marginal tax on saving of 260 percent; for each additional dollar saved, the parent loses $2.60 in additional taxes and forgone government benefits.

By contrast, if the same parent earned $250,000, the marginal tax on saving would be only 31 percent.