Ezra Klein offers up some mandate analogies:
First, Obama aside, mandates matter because, sometimes, folks have to be protected from their worst instincts. That's why we force everyone to pay into fire departments through taxes. Otherwise, some folks would opt out under the theory that they don't do much cooking, and we don't want their houses to burn down.
Second, single payer, which so many folks love, is a mandate by a different name. That name is taxes. Some people will feel they can't, or shouldn't, pay that level of taxes, and they will be angry, just as some will feel they can't afford insurance, or shouldn't have to buy it, and they will be angry. Now, maybe single payer is a better way to structure the mandate. But it's a mandate nevertheless.
But there's a clear difference between providing a universal public service (fire department / single-payer) financed through progressive taxation, and between setting up a bunch of private for-profit firefighting firms and then forcing everyone to buy their services (health care mandate / weird quasi-libertarian dystopia). We're obviously not going to run a government policy in any are without "mandating" that some people do some stuff, but that's hardly the same as saying that mandating that people buy specific kinds of products from for-profit firms is a close substitute for public provision of goods.
This is why, to me, it's unfortunate that the discussion initially kicked off by John Edwards' health care proposal has tended to focus so heavily on the mandate issue and touch so lightly on the idea of introducing a public sector health care alternative to compete with private plans. That's a very good idea in my view, but obviously there are a lot of important details to be worked out. What's more, unlike making people buy health insurance, this is an idea insurance companies will really hate -- propose a substantial reform and I'm sure the insurers will tack a mandate on. But it's an idea I'd like to see the next president really fight for. What I don't want to see happen is the president come in having promised so loudly to pass "a health care bill" that he or she then feels absolutely compelled to agree to whatever the 41st most conservative senator will agree to even if that means a bad bill.
In terms of a mandate's relationship to single-payer, the point is that in order to make a robust public sector option viable, you either need a mandate or else you need to finance the public sector option with tax dollars which, as Ezra says, is a kind of mandate. But that all depends on the public-private competition actually being there. Absent it, what you have isn't anything like single-payer, it's a kind of large subsidy to insurance companies.
*[let me now note that even though the primary campaign has tended to swallow everything and what follows dissents somewhat from the Clinton line on mandates, I still think she has the better proposal at the end of the day]
UPDATE: See also Brian Beutler on legislative dynamics. To be clear, though, this post is not aimed at boosting Obama's fortunes vis-a-vis Clinton since I think they both have a similar problem here. The crux of the matter is that we don't want the next president to head into negotiations in such a way that he or she can't say no to any kind of "health care bill" that emerges. Reform is important, but it needs to actually be reform that makes things better not reform for the sake of "doing something" about the problem.