The public option thrown around by Obama is intended to be a true comprehensive alternative to private healthcare. The problem with this is that it will have the ability to quash any competition with private insurance, leading to monopsony. That will reduce quality of care for everyone as doctors exit, demand for doctors increases, and research declines. True universal healthcare in the US is ill-conceived at best.
However, because healthcare is a good that you do want people to consume some of, perhaps a discount level of health insurance is a good idea. Instead of being comprehensive, this discount health insurance could serve to fund the basic healthcare steps that you want to incentivize everyone to get without covering every single health ailment.
This addresses the problem of "rising health care costs", which are a function of the fact that we can treat so many more things now that we never used to be able to treat. For example, chemotherapy didn't exist 30 years ago, and it's expensive. People back then didn't have to pay for chemotherapy because they couldn't get it, so their medical costs were low.
It's a basic law of economics that you can't reduce price without reducing the incentives of providers to provide, which is a major negative. But if you offered a form of discount health insurance to people just for basic care, or just for catastrophic care, the premiums would be much lower without killing quality of care. People with no healthcare could now "buy in" to a small amount of healthcare for a much cheaper rate, presumably increasing the healthcare provided.
In other words, think of healthcare as a separable good - you get basic care (checkups, antibiotics, routine health problems) and catastrophic care (cancer, emergency surgery, etc). You can also separate it into getting older forms of care and getting cutting edge forms. Healthcare is comprised of many goods and services, and someone with more knowledge of different services and goods could probably come up with different packages of insured and uninsured procedures and medicines taht would be cheaper but still much more attractive than nothing.
Currently, it is only offered completely packaged, because most people want packaged care. As packaged care gets better, it gets more expensive - so why not offer more options?
You could have a Basic Care option, where catastrophe means you dont get care but you get covered on basic stuff. You could have a catastrophe care option, more along the lines of typical insurance in other fields- you pay for the basic stuff but if you're faced with anything huge, you're saved. You could have a "turn back time" option, where you get access to the same quality of care you would have had 15 years ago when everything was cheaper - you get basic care, and then the less expensive forms of catastrophe care.
The variations can go on, and this can be provided privately. An extremely baseline option could even be public care without compromising quality of care very much, because you shouldn't see many people moving from comprehensive care down to the baseline government care, but you would move everyone with no care up to the baseline government care.
For example, imagine the government offered coverage only for basic antibiotics, trauma surgery, rehab for smoking/alcohol/drugs, diabetes treatments, heart attack/stroke treatments, lung, prostate, breast, testicular, colon, skin and maybe a few more cancer treatments, and regular physicals, mammograms or enemas.
There are certainly many things that would go uncovered... but this is a basic list encompassing a very large number of the problems that people have. You could offer those treatments for a fraction of the cost of regular healthcare and still ensure that most people are covered for most of the problems they're going to have. Nobody with full healthcare would want to shift down, but it's a darn sight better than no healthcare at all. Costs stay low for these people, while still providing them with some healthcare, and without impacting the R&D machine that has so improved the quality of medical options in the US over the last 30 years.
EDIT: you can actually even have a situation where insurance covers the common stuff for low deductible, and then everything else for very high deductibles. That way, with a stretch, you may even have everyone able to afford things. I haven't worked with that idea that much (and there is plenty of potential for screwing it up) but it's just an idea