Romney's own position is as clear as mud. I have read his comment here very SLOWLY and I absolutely cannot parse what he actually means.
At a recent town hall event captured by CNN, a woman stood up to ask about Romney’s views on private social security accounts like the ones proposed by former President George W. Bush. Romney said he has described the options for Social Security but that he opposed privatization in Social Security and said that he’s instead in favor of letting some people save a portion of their income tax-free:
WOMAN: If I understand it correctly, that you say part of Social Security, one way of doing it is privatizing, that people can invest their money, is that correct?
ROMNEY: I didn’t mention that. There are ideas, I didn’t mention that. I just described the three major ones. There have been other ideas about people investing. You know, the disadvantage, privatization of Social Security, that doesn’t make sense. I mean, privatizing Social Security. There have been some that have said let people save some of their money and let them invest it. The market goes up and down. I kind of like the system the way that we have in that regard. It would be nice if people could take a portion of their income and save it tax-free.
http://thinkprogress.org/economy/2011/08/26/305277/romney-private-social-security/Think Progress seems to have the same difficulty.
Here is his answer in pro privatization answer in 2008:
Q: Will you do for Social Security what Reagan did in 1983?
A: I’m not going to raise taxes. Not only are you taking money away from their pocketbooks, you’re also slowing down the economy. You slow down the economy, more people lose work. More people lose work, of course, you’re having a lot of folks that really have their lives turned upside down. So, raising taxes is just something you don’t want to do. We’re going to have to sit down with the Democrats and say, let’s have a compromise on these three elements that could get us to bring Social Security into economic balance. You can have personal accounts where people can invest in something that does better than government bonds--with some portion of their Social Security. We’re going to have the initial benefit calculations for wealthier Americans calculated based on the Consumer Price Index rather than the wage index. That saves almost two-thirds of the shortfall. You can change the retirement age. You can push it out a little bit.
http://www.ontheissues.org/2008/Mitt_Romney_Social_Security.htmHere he is in an August 2011 article - now saying "no" to social security, but for letting people earning under $250,000 save tax free - as TP pointed out that is what a 401K already does - so he is likely thinking of the higher income people in that group who might want to save more than the 401K limit.
Note that he prefers lower benefits or a higher age to raising the income cap.
http://www.boston.com/Boston/politicalintelligence/2011/08/romney-greeted-protestors/f6mMTOy14WQVj5b871PWXO/index.html