My short answer is yes. No, not right now since it would only confuse things. But during his first administration? Absolutely.
And for all those worried, this is a perfectly progressive position. Let me explain.
Let's start with the basics. What is Social Security (SS)? It's the government forcing you to save for your old age. Well, that and a little more since it also includes life and disability insurance.
Originally that was the real SS debate. Should government force people to save if they did not want to? Friedman is a good example of an outspoken critic of the the government making savings mandatory. The pro SS side realized that, left to their own devices, millions of Americans, through lack of planning or misfortune would not save enough for retirement and we, as a society, could not stand by and let millions of seniors slide to poverty.
That debate is now over. We have won. I'm sure there are many on the right that still wish to get rid of forced savings altogether but it will not happen. And not because of anything the Democrats may or may not do. It won't happen because voters don't want that. Any policy that leads to a dramatic increase in poverty among seniors will quickly destroy the political party that supports it.
The new debate on SS is no longer about ends, but about means. Society has reached a consensus that the government needs to ensure a minimum well-being for seniors. Where we don't have a consensus is on the best method to achieve that.
Properly defined, there is no reason why Democrats and liberals should not favor privatization. Allowing people more control over their retirement money is a good thing. Of course, we need to ensure that during the transition nobody gets lost and that current and about-to-be retirees are paid what they were promised. These transition costs will have to financed through a combination of tax increases and borrowing. I can think of no better way for the Democrats to oppose making Bush's tax cuts permanent then by combining greater choice for retirees with a need to strengthen SS for those in it today. This creates a great coalition of seniors that don't want to lose SS and younger people that are comfortable with managing their retirement funds.
But what if people mismanage their funds and end up losing much or even all of their savings? This is a good question and the answer tells me that conservatives that favor privatization have not fully realized what this will entail.
Several nations have privatized SS (or its local equivalent) mainly in Latin America. And the one clear lesson we can draw from it is that it requires heavy government regulation on what you can or cannot invest in. If the purpose of forcing people to save is to ensure a minimum amount of retirement income it simply makes no sense to allow a situation where they may lose that. Therefore government must limit what can be invested and where, mostly in some sort of index fund, or maybe a basket of funds that varies in risk based on the contributor's age.
Can conservatives try to get around this and allow anyone to invest as they wish? They can try but it will only backfire. Sooner or later some people will make mistakes and there will be an uproar to bail them out.
In the end, since we (mostly) agree that government has a role ensuring seniors' well being there is no reason not to consider more modern methods to reach that goal.
Update
It seems this topic touches a raw nerve for many. There appears to be what could be described as an emotional attachment to what is, after all, just a policy program.
As for some of the concerns, I'll see if I can address them.
Why do this?This strikes me as the wrong question. The correct question to ask is, what is the best way to provide what we want SS to provide. No economist would propose something like SS if it were being created today. It made sense 50 years ago when we did not have the financial instruments we have today and, more importantly, we had a very, very different demographic structure. We've all seen the charts of active workers to retirees and how the ratio has fallen dramatically in the last decades and will continue to fall in the future. SS is in no immediate danger but that doesn't man that it's the best program possible. It isn't.
How do we pay for it? This is actually simple. We could easily borrow the whole amount, if we so needed. US Government debt held by the public is actually pretty low, at around 36% of GDP. Many of our peers have ratios closer to 100%. There is no lack of capacity to pay for it. And, of course, we can rescind Bush's tax cuts.
This is a ripoff. This, I admit, I don't understand. Ripoff? Who is ripping of whom? If any of us could invest our SS taxes into a 401K we would get much, much more money than we will from SS. The only problem is the transition cost since we need to pay for those that are already retired or close to it. Someone posted that this is a scam to sell off public resources. What public resources? There are none here. It's our money that we can use in different ways. There is no ripoff here.
It would eliminate a safety net. Not at all. Why would it eliminate the safety net? In fact it will increase it since you would get more money than you can currently expect under SS. Even allowing for some bad periods any relatively safe portfolio will greatly outperform the current return from SS. Yes, government will have to regulate it but government already regulates SS so what's the difference. And as a commenter pointed out you could invest it all in Treasuries making it basically risk free and it would have the exact same backing as today's SS does (federal taxes).
Finally, it seems I confused things a bit when I posted that SS forces us to save. Technically we pay for the previous generation and then the next one pays for us. But I think the basic point is the same. Government forces you to make some payments so that you get paid back some other amount for retirement.