It would certainly be difficult to build a self sufficient Mars colony, but I don't think it's impossible. I agree that there would be a long time between the first landing and a self sufficient colony.

I'm not so certain self-sufficiency is possible. Humans are an animal in an ecosystem that sustains it, no matter how much we might kid ourselves otherwise. We aren't self-sufficient on Earth, but deeply dependent on our environment. There is a distinct chance we'd always need things from it. Besides biodiversity that couldn't exist on Mars, there are many natural resources that are a product of that ecosystem that Mars would never have. The needs for food, raw materials that are the basis for most medicines, natural materials for daily life (like wood, paper), and the loss of access to a biodiversity that has been central to human survival are something that I don't think there's any guarantee could be ever be replaced on Mars, though since I don't think there's any possibility of humans surviving there ever, it's kind of peripheral.

The longest a group of humans have gone without depending on earth's biosphere is 2 years [http://en.wikipedia.org/wiki/Biosphere_2], so I suppose you are allowed to be skeptical. I am not skeptical, let me explain why. In the biosphere 2 experiment the 8 subjects lost weight the first year as they figured out how to manage an ecosystem, but they gained weight the second year. They could have kept going for significantly longer if they wanted to.

The first step would be a colony that can produce and clean its own air and water and some of its food. This seem achievable in the near term. The second step is a full ecosystem (needs almost no nutrients from earth), which is much harder but I think biosphere 2 is a good proof of concept. Mars is much colder with less sunlight so it is a much harder problem on Mars. The finial step is an independent industrial base. You mentioned medicine, but I'm more concerned with the microprocessors to keep the automation running. Humanity can survive without medicine, and with a few easy things like penicillin we can do quite well (we can also avoid bringing the majority of diseases to Mars in the first place). Without automation I don't think one person can produce enough resource to sustain themselves in such a hostile environment.

Self-sufficiency is hard and I think a million people is a good estimation of how large a Mars colony would be before it became truly self sufficient.

I don't think Biosphere 2 is a great example. In Mission 1 there were huge problems regulating CO2 and O2, their pollinators died, invasive insects took over, and they had continually increasing NO2 and CH4 gases. They eventually injected O2 from outside to make up for the decreasing levels, and when a participant got sick, they smuggled supplies back on their return. It was a disaster. And they had a door they could open to walk out.

The issues with getting something like an ecosystem on Mars would be much more dramatic, esp. given that while there are some ways of getting O2 and carbon, there isn't a source of nitrogen on Mars that we know (we assume there's fixed nitrogen in minerals, though that's very hard to breathe). Any loss of significant life forms would need to be replenished from Earth. And while some life forms will probably manage in 38% gravity, there's no reason to assume many would have long term viability (especially vertebrates like humans who depend on Earth gravity to function).

Getting an ecosystem on Mars that could support humans doesn't seem like it's in the realm of possibility to me, especially when there's good reason to believe humans themselves wouldn't be able to survive for long periods there unless something managed to solve that very hard problem. You could use a centrifuge for the long trip out (and nobody could survive without that), but you can't just live in a centrifuge on Mars forever.