Right now, everyone is obsessed with the high cost of health care, and there is much weeping and wailing about the costs and how to solve the problem. It sounds absurd to think that sending humans to Mars could help with this, but there is a connection.
One of the requirements for sending humans so far away from home is going to be a small, compact, medical diagnostic system. If any of the astronauts becomes ill, they can't run to a doctor for treatment, they need to have a way of running all the standard tests on the mission. A med unit would solve this problem.
It would also be a huge benefit here on Earth. Such devices are slowly being developed for Third World nations, however, the potential profits from sales to those nations would be rather small, so the amount of R&D being devoted to them is minuscule. Furthermore, since the primary application of those devices is seen as being in the Third World, most Americans are unaware of research efforts in that area.
Now to the debate on health care in the US, one of the issues being raised is how much it all costs. An automated system, which works well enough to perform standard diagnostic tests millions of miles away from home, or in a developing nation, is certainly capable of replacing a doctor visit when one has something like the flu.
Since it is highly likely that any manned mission to Mars will be closely followed by the general public (not merely in the US, but all over the world), astronauts using a med unit will attract a great deal of attention. This will inspire both individuals and insurance companies to bring pressure to bear and make these machines available to the general public.
No doubt there will be considerable opposition to the widespread use of the devices from groups like the AMA, but with the combined weight of the general public and the insurance lobby, it seems almost certain that this will fail. A side benefit, besides lowering the cost of health care for the general public, the greater demand for the machines will lower the cost of each individual unit, making it easier for developing nations to purchase more of the devices.
Granted, it may not immediately occur to people that such a device could take the place of their doctor for most routine visits, but it certainly will occur to someone in the insurance industry, and if an astronaut says something like he wants one of those things when he gets back home, many more people will pick up on the idea.
If the units are relatively ubiquitous, and having a series of tests run costs a modest amount, like say $5, not only will people be inclined to use them when they know they are sick, but if they're at the pharmacy (or somewhere else one might expect to find one of the machines), they're liable to give it a whirl, simply for entertainment value. If the machine spits out a result indicating that they have a potentially serious condition, even though they haven't begun to display any symptoms, the machine might well be a lifesaver for them. Many cancers and other illnesses are easily treatable if caught early enough.
Additionally, by collecting data (stripped of any personal identifiers to help preserve privacy) on large groups of people, epidemiologists can better track the spread of disease, as well as being alerted to potential outbreaks of new strains of flu, or other diseases far earlier than they are now.
Doctors will still be needed to oversee treatment of a number of different illnesses, as well as handling such procedures as surgery or setting broken bones, but the machines will reduce much of their workload, enabling them to spend more time with each patient that they see. Additionally, the diagnostic machines will help individuals better manage their health, in conjunction with their doctor. They will be able to do more frequent monitoring of their health, and this will enable the doctor to better adjust the treatment based on more frequent test results.
Again, there are those who will argue that none of this requires a manned mission to Mars to happen, but this ignores the reality of human behaviour. The need for such devices, in the developing world at least, is great, and probably obvious to the people who provide medical care in those areas. It is not, however, obvious to enough folks with the necessary resources to design and build such a machine. Nor is it readily apparent that such devices could benefit those in the developed world, who have more or less ready access to medical care. Putting it up on the world's radar by showing it being used on a manned Mars mission will drive home the fact that everyone on the planet could benefit from such machines being readily available.